DOCUMENT RESUME

ED 069 666 211 TM 002 115 AUTHOR Havlicek, Larry L. TITLE An Empirical Investigation of Specified Violations of the assumptions Underlying Statistical Techniques. Final Report. INSTITUTION Kansas Univ., Lawrence. School of Education. SPONS AGENCY Office ofEducation(DREW) , Washington, D.C. Regional Research Program. BUREAU NO BR-1-G-060 PUB DATE Mar72 GRANT OEG-7-71-0021 (509) NOTE 202p.- EDRSPRICE MF-$0.65 HC-$9.87 DESCRIPTORS *Analysis of ; *Correlation; Educational Research; *Evaluation Techniques; Hypothesis Testing; Measurement Techniques; Research Methodology; Research Reviews (Publications) ;; Statistical. Bias; *Statistical Studies; Tables (Data); *Tests

ABSTRACT The purpose of this study was to empirically determine the effects of quantified violations of the underlying assumptions of parametric statistical tests commonly used in educational research, namely the correlation coefficient (r) and the t test. The effects of heterogeneity of variance, nonnormality, and nonlinear transformations of scales were studied separetely and in allcombinations.Monte Carlo procedures were followed to generate random digits which had the following shapes: normal,positively skewed, negatively skewed, and leptokurtic. Interval, ordinal, and rank transformations were used for all of the computations which were based on5,000sets of randomly generated numbers, each set containing either 5, 15, or 30 such numbers. A total of1,332 combinations of differences in shape of distribution, variance, size of sample, and type of scale were studied. The resultsindicate that the distribution or r do not deviate significantly from the' theoretical distributions even under the most severe combinations of violations. However, there were many significant discrepancies for the t test. The results of this study lead to theconclusionthat 4.-..he t test is not as robust as generally thought and thatresearchers should consider all of the basic assumptions before applying this test to their data. (Author) 0. .1 4 -; (71 G.' (: (-

U.S. OEPARTMENT OF HEALTH. EOUCATION & WELFARE OFFICE OF EOUCATION MIS 00CUMENT HASREIN R11110 IIUCIO EXACILY AS MCIIVED I ROM THE PE itt,uti OR 011GANIIATION FINAL REPORT ORIG INATING U POINTS orVIEW OR OPIN IONS SIATEO 00 NOF NECESSARILY REPRESENT OFFICIAL OrEICEOF EOU CATION POSITION OR POLICY

Project No. 1G060 Grant No. OEG -7 -71 -0021

Larry L. Havlicek School of Education University of Kansas Lawrence, Kansas 66044

AN EMPIRICAL INVESTIGATION OF SPECIFIED VIOLATIONS OF

THE ASSUMPTIONS UNDERLYING STATISTICAL TECHNIQUES C

4 . March 1972 t Ef4

U.S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE

Office of Education

National Center for Educational Research and Development (Regional Research Program) Abstract

The purpose of this study was to empirically determine the effects of quantified violations of the underlying assumptions of parametric statistical tests commonly used in educational research, namely the correlation coefficient (r) and the t test. The effects of heterogeneity of variance, nonnormality, and non- linear transformations of scales were studied separately and in all combinations.

. Monte Carlo procedures were followed to generate random digits which had the following shapes: normal, positively skewed, negatively skewed, and leptokurtic. Interval, ordinal, and percentile rank transformations were used for all of the computations which were based.on 5,000 sets of randomly generated numbers, each set containing either 5, 15, or 30 such numbers. A total of 1,332 combinations of differences in shape of distribution, variance, size of sample, and type of scale were studied.

The results indicate that the distributions of r do not deviate significantly from the theoretical distributions even under the most severe combinations of violations. However, there were many significant discrepancies for the t test. The results of this study lead to the conclusion that the t test is not as robust as generally thought and that researchers should consider all of the basic assumptions before applying this test to their data. FINAL REPORT

Project No. 1G060

Grant No. 0EG-7-71-002.1(509)

AN EMPIRICAL INVESTIGATION OF SPECIFIED VIOLATIONS

OF THE ASSUMPTIONS UNDERLYING STATISTICAL TECHNIQUES

Larry L. Havlicek

School of Education University of Kansas Lawrence, Kansas 66044

March 1972..

The research reported herein was performed pursuant to a grant with the Office of Education, U.S. Department of Health,.Education, and Welfare. Contractors undertaking such projects under Government sponsorship are encouraged to express freely their professional judgment in the conduct of the project. Points of view or opinions stated do not, therefore,-necessarily represent official Office of Education position or policy. .

U.S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE

Office of Education National Center for Educational Research and Development (Regional Research Program)

ii 1111151111111111117111111111MPINRWRTIF

I would like to express my indebtedness to Mrs. Judith S. Halderson for the many hours she spent writing the computer programs, checking computations, and insuring that the results were accurate and valid. She was primarily responsible for the development of all of the computer programs, which she did very efficiently and effectively. She also provided valuable help, advice, and collaboration on all other aspects of the study. The assistance of the University of Kansas Computer Center staff is also appreciated. Jim Frane's assistance in developing the computer routines to generate the distributions of scores and John Kocourek's assistance in running the analyses merit special mention.

To researchers in all areas, we hope that this study will make a contribution toward better understanding of the application of the t test and the correlation coefficient in situations in which violitions of the basic assumptions may be, suspected. To accomplish this, the results are presented in a non-technical, as-they-occurred fashion. It is suggested that researchers compare the conditions under which these analyses were computed with the conditions they are working under and then decide whether or not t or r is appropriate for their analyses.

iii TABLE tit CONTENTS

Page

Abstract

Title Page ii

Preface iii

Table of Contents iv

Groupings of Tables

Introduction 1

Purpose of the Study

Related Research 2

Procedure 7

Results 13

Distributions of t for Samples from Normal Distributions 17

Distributions of t for Samples from Normal and Skewed Distributions 21

Distributions of t for Samples from Positively Skewed Distributions 25

Distributions of t for Samples from Positive and Negative Skewed Distributions 27

Distributions of t for Samples from Positively Skewed and Leptokurtic Distributions 29

Distributions of r for all Populations 31

Summary and Conclusions 33

Bibliography 37

Appendix A: Population Values and Distributions

Appendix B: Tables of Sampling Distributions ofthe t Ratio

Appendix C: Tables of Sampling Distributions of theProduct Correlation Coefficient Groupings of Tables

Page

Summary Table 36

Appendix B: Tables of Sampling Distributions of the t Ratio

Normal and :formal Distributions: Equal n's B- 1 Unequal n's B- 8 Normal and Positive Skewed Distributions Equal n's B- 20 Unequal n's B- 30 Normal and Negative Skewed Distributions Equal n's B- 42 Unequal n's B- 50 Normal and Leptokurtic Distributions Equal n's B- 56 Unequal n's B- 62 Positive Skewed and Postive Skewed Distributions Equal n's B- 68 Unequal n's B- 78 Positive Skewed and Negative Skewed Distributions Equal n's B- 90 Unequal n's B-104 Positive Skewed and Leptokurtic Distributions Equal n's B-116 Unequal n's B-120 Negative Skewed and Leptokurtic Distributions Equal n's B-123 Unequal n's B-127 Leptokurtic and Leptokurtic Distributions Equal n's B-130 Unequal n's B-134

Appendix C: Tables of Sampling Distributions of the Product Moment Correlation Coefficient

Normal and Normal Distributions C- i.

Normal and Positive Skewed Distributions C- 5

Positive Skewed and Negative Skewed Distributions C- 9

v Introduction

In the behavioral sciences, the most commonly used are those for measuring the degree of relationship between two variables and those for comparing sample . the statistics most frequently used are, respectively, the Pearson product moment correlation coefficient and the F test or equivalently the t test when there are only two groups.

For the mathematical justification of hypothesis testing procedures, these tests are based on a number of assumptions as enumerated by Guilford (1965), Ferguson (1966), Hays (1963), Lindquist (1953), and Siegel (1956). Specifically, the assumptions for the correlation coefficient are: (1) the trend of the relationship between X and Y be rectilinear, (2) the variables must have been measured by at least an interval scale, and (3) the bivariate distribution is normal.The assumptions necessary for the statistical tests for comparing means are: (1) the observations must be independent, (2) the observations must be drawn from normally distributed populations, (3) the populations must have the same variance (homogeneity of variance), and (4) the variables involved must have been measured by at least an interval scale.As stated by Siegel (1956), Cochran (1947), and Cochran and Cox (1957), a researcher can never be sure that all of these assumptions are met and often there is good reason to suspect that some are false.Thus, as Kirk (1968) points out, parametric tests should be regarded as approximate rather than exact when it is known that all of the assumptions have not been met.

If the researcher has reason to suspect that any of the necessary assumptions are violated, he has his choice of either going ahead with the parametric test, resorting to a less powerful distribution-free statistical test, or using a data transformation. However, in regard to the second approach, Hays (1963) and Boneau (1959) have pointed out that two things must be considered when substituting distribution-free techniques for parametric procedures: (1) the actual hypothesis tested by a given distribution-free test is seldom exactly equivalent to the hypothesis tested by the parametric test and (2) distribution-free tests have the disadvantage of being relatively low-powered as compared to parametric tests. This means that, other things being equal, a relatively larger sample size is required as compared to the parametric method if Type II errors are to be held to a minimum. With regard to transformations, Anderson (1961) states that it is possible to get a significant F ratio from the original data and not from the transformed data, and vice versa. Bradley (1968) states that tranformations may reduce the power of the statistical test through the homogenizing effect and also may be restricted to the case where the null hypothesis is true. Also, as pointed out by Kirk (1968), once an appropriate transformation has been made all inferences regarding treatment effects must be made with respect to the new

1 scale not the original scores.

Confronted with the problem of whether or not to use a distribution-free statistical test orperhaps an equally discouraging one of using a transformation, performing related tests, and then having difficulty in interpreting the results, the researcher is often tempted to ignore the assumptions of the parametric tests and apply these tests to his data. If the researcher decides to use a parametric knowing that one or more of the assumptions are violated,what are the consequences? If the statistic indicates a significant relationship or difference, is this due to real relationships or differences or is it due to the violation ofassumptions? The latter possibility is considered by many researchers as sufficient to preclude the ut.e of the parametricstatistic.

Purpose (4 the Study

The overall purpose of this study was to study the effects of combinations of violations on parametric tests.' Specifically, the purposes were:

1. To empirically determine the effects on r and t due to violations of the assumptions of normality, homogeneity of variance, and measurement properties separately aud in combination; and

2. To establish guidelines for determining the resulting effect of the violations based on measures of those violations.

Related Research

Although the effects of certain violations of assumptions on parametric tests have been studied quiteextensively, there persists a disagreement as to the seriousness of those violations. Bradley (1968), Senders (1958), Siegel (1956), and Stevens(1951) have asserted that the effect of violating atest's necessary assumptions is to render the test inexact, often leading to inaccurate and meaningless conclusions. The advocates of strict adherence to the basic assumptions underlying the parametric tests argue that the meaningfulness of the results ofparametric tests depend on the validity of all of the assumptions.Anastasi (1961), Eisenhart (1947), Senders (1958), Siegel (1956), and Stevens(1951) believe that can only be used withinterval data and contend that analyses would be in error to the extent that the successive intervals on the scale are unequal insize. They also point out that failure of meeting the assumptionsof normally distributed scores and homogeneity of varianceswould affect both the significance level of the test and thesensitivity of that test.

2 Bradley (1968), as one of the leading spokesmen for distribution-free statistical tests, has asserted that "any violation of a parametric test's assumptions alters the distribution of the test statistic and changes the probabilities of Type I and Type II errors" (p. 25). In criticizing advocates of Parametric tests when there are known violations, he speaks of the "Myth of Robustness" in which he refers to the lack ofan agreed-upon connotative meaning of robustness.

The most insidious thing about the Myth of Robustness, however, is that the "degree" of a test's robustness against violation of a given assumption is strongly dependent upon factors which are not involved in the statement of a test's assumptions, which are often not required in a complete description of the assumption's violation, and which are not mentioned in the usual

allegation of robustness, as quoted above. These , factors cause no distortion of Type I or Type II errors viten all assumptions are met, but greatly influence the distortion occurring under a given violation of assumptions, i.e., the factors interact with whatever violation occurs. (Bradley, 1968, p. 26)

He goes on to state that many studies of the effects of violations of assumptions have investigated analyses in which only one assumption was violated and/or where some of the important interacting factors were "held constant."lie makes a well- founded criticism of these studies by stating that they do not specify the amount of violation nor do they consider the fact that there is a strong tendency for these violations to interact with one another. lie goes on to point out that for a given violation of assumptions, none of the factors relative to sample size, shape of the distributions, significance level, or relative appear to exert its influence upon probability levels independently of all other factors. Thus, depending upon the particular combination of factors and their particular levels or values, a given violation of assumptions occurring in a. specified degree may have a negligible or devastating effect upon the probability levels of the statistic. He also points out that many of these studies do not take into account "outliers" and what effect these extreme scores have on parametric tests.

Opposing the point of view of those who advocate strict adherence to the basic assumptions are a number of statisticians, e.g., Lord (1953), Hays (1963), Anderson (1961), McNemar (1962) and Lindquist (1953), who have argued that for the majority of studies the effects of violations of the basic assumptions are not sufficiently great to invalidate the statistical test. However, often there are qualifiers to the statements about the effects of assumption violations. For example, Dixon and Massey (1957) state that the results of the analysis of variance are changed very little

. 3 by "moderate" violations of the assumptions of normaldistribution and equal variance. Ferguson (1966) indicates that unless there are "extreme" departures from normality,there is no serious effect on the analysis of variance F ratio. Hays (1963) contends that even when the forms of the populationdistributions depart "considerably" from normal, the inferences made about means are valid providing the number of cases In each sample isthe same and fairly large. In summarizing the results of the Norton study, Lindquist (1953) interprets the results of thisstudy co that

. . .one need be concerned hardly at allabout lack of symmetry in the distribution of criterion measures, so long as this distxibution is homogeneous in bothform and variance, and sc long as it is neither"markedly" peaked nor "markedly" flat (p. 86) .

Box (1953) states that there is abundantevidence that the parametric tests for comparing means are remarkably insensitive to"general" non-normality of the parent population.He goes on to state that by "general" is meant that the departure fromnormality is the same in the different groups. However, if the is in different directions, larger effects nre often found. As Bradley (1968) has indicated, such unquantified,ambiguous statements concerning the degree of violation ofassumptions has led to serious misunderstandings concerningthe effects of the underlying assumptions and provides nodifferentiation between "ordinary" and "extraordinary" degrees ofviolation.

With regard to the types of measurementscale needed for parametric tests, a number of statisticians haveindicated that parametric tests do not require interval data. As Anderson (1961), Burke (1953) and Lord (1953) point out, the validityof a parametric does not depend on the type ofmeasuring scale used. These authors believe that statistics computed on a measurement scale which is at best a poorfit to reality distribute in the same way that they would underconditions of perfect measurement.

Several empirical studies have provided supportfor the above position. Probably the best known study is that of Norton (1952). Norton's technique was to obtain iistributions of F ratios by means of a random sampling procedurefrom distributions having the same mean but which violated the assumptionsof normality and homogeneity of variance inpredetermined ways. As a measure of the effect of the violations,Norton compared the obtained percentage of sample F ratioswhich exceedeu the theoretical 5% and 1% values from the F tables forvrrious conditions. The discrepancy between the obtained percentagesand the theoretical percentages was used as the measureof the effects of the violations. Six different forms of distributions were studied under two different sample sizes and withvarious combinations

4 of variance. The results may be summarized as follows:

1. When the samples all came from the same population, the shape of the diftribution bad wry little effect on the percentage cf. F ratios e:.:ceeding the theoretical limits.

2. For sampling from populations having the same shape but different variances, or having the same variance but different shapes, there was little effect on the empiripal percentage exceeding the theoretical limits.

3. For sampling from populations with different shapes and heterogeneous variances, a serious discrepaftcy between theoretical and obtained percentages occurred in some instances.

Using a similar procedure, Boneau (1959) compared obtained distributions of sample t values with the theoretical dietribution of the t statistic. Random samples were drawn from populations which were either normal, rectangular, or exponential with means equal to 0 and. variances of 1 or 4. For several combinations of forms and variances, t tests were computed using combinations of sample sizes 5 and 15. Comparing his sample didtributic. of 5000 t values, Boneau concluded that the t test is "remarkably robust" in the technical sense of the word to violations of a number of assumptions underlying that test, providing that (1) the two sample sizes are equal or nearly so and (2) the assumed underlying population distributions are of the same shape or nearly so. If these conditions are met, then the percentage of times the null hypothesis will be rejected when it is actually true will tend to be between 4% and 6% when the alpha level is 5%. However, if there is a combination of unequal sample size and unequal variances, probability dig.tKiin.tions may be quite different from the theoretically expected values.

In another study of the t distribution, Baker (1966) compared the of t based on one set of scores with the sampling distribution of the same statistic based on scores which were not "permissible" transformations of the first set. If violations of measurement scale properties have an effect on the t distribution, then the sampling distributions computed under conditions of "perfect" measurement should differ from the same statistic based on "imperfect" measurement. In order to evaluate the consequences of non-permissible transformations, 35 non-linear transformations of a unit-interval set of scores were constructed. The first 15 transformations were constructed to simulate the situation in which the magnitudes of trait differences represented by ,intervals at the extremes of a scale may be greater than those represented by equal appearing intervals in the middle of the scale, e.g., percentile equivalents. The third set of transformations were such that the first scores ranging from 1 to 15 were retained as interval but the remaining scores varied randomly, similar to scales sometimes found in social distance measures or in the Thurstonetype of scaling of attitude items. A total of 36 t values were computed for each pair of samples drawn: one value for the unit-interval scale andone for each of the 35 transformations. Three types of distribution were studied -- normal, rectangular, and exponential--and three sample sizes were used--5 and 5, 15 and 15, and 5 and 15. The combinations of sample sizes used were identical to those used by Boneau (1959). Empirically derived t distributions based on 4,000 random samples for each condition were found not to deviate from the theoretical 5% or 3% levels of significance providing that the pair of samples are of equal size and that a two-tailed test is used. The authors conclude that probabilities estimated from the t distribution are little affected by the kind of measurement scale used.

Norris (1960) conducted an extensive study on the differential effects of nonnormality on the Pearson product-moment correlation coefficient. Comparisons were made between the theoretical sampling distribution based on Fishers' z transformation and empirical sampling distributions from nonnormal populations as well as comparing the latter distributions with distributions of r from his normal distributions. The latter comparison would show the effects of nonnormality. To indicate the effects of different conditions, the comparisons were made separately for various types and degree of nonnormality, three different samples sizes (N = 15, 30 and 90), and two markedly different population correlations (r = .0 and .8). Five forms of distributions were studied:normal, rectangular, leptokurtic, slightly skewed, and markedly skewed. Deviations of obtained distributions from the theoretical distributions were tested by the use of the Kolmogorov-Smirnov goodness-of-fit test (Siegel, 1956). The results of this investigation led Norris to conclude that the effect of nonnormality should be taken into account when dealing with statistical tests of inference involving the product moment correlation coefficient. He suggested that more research was needed, especially with regard to other types of nonnormality and with populations not having identical marginal frequencies such as he studied.

The four studies summarized above indicate that violations of certain assumptions do not drastically alter the distributions of the parametric statistic studied. However, there are certain restrictions in these studies since they are limited to the specified violations and other specific conditions such as sample size, degree of variance, and form of distribution. For example, in the Boneau (1959) study, the of variance of scores studied was limitedfl and 4, and the distribution of t's was based only on 1,000 t's. The other three studies were also based on violations which deviated in specified ways. Although the results of these studies can be applied to situations in which the violations of assumptions are similar, there are still questions concerning situations in which other combinations of violations are commonly found in educational research.

6 Procedure

The procedure that was followed in this study was based on a Monte Carlo method of generating sequences ofrandom numbers one at a time as they are required. As pointed out by llammersley and Handscomb (1965), such pseudorandom sequences of numbers are most convenient to calculate when working with an electronic digital computer, and such numbers are appropriate for probabilistic types of studies. For this study, computer routines were utilized to generate numbers which were distributed in four basicshapes: normal, positively skewed, negatively skewed, and leptokurtic. The final program called for these routines as they were needed.

The first stage in the overall procedure was to generate four basic populations of scores each with N = 10,000. These four populations were distributed as noted above and initially each population had a mean of 0 and a of approximately 1. transformations were then used to produce populations with means of 50 and standard deviations of 4, 8, and 16.

Four function routines were used to generate thepopulations of numbers. The was generated using the function RMS(IST) which was developed at the University of Kansas Computation Center. The argument IST is a 10-digit odd number originally specified by the user and was different for each analysis. The positively skewed distribution was generated by the function routine PSK(IST). This function generates a ICz value from the distribution of chi square with mean = 3 and variance = 6, the shape of which is positively skewed. The function calls RMS(IST) to obtain the normal variates used to find'X2. The value returned is standardized to a mean of 0 and a standard deviation of1. The negative skew function, RNSK(IST), is equal to -1 timesPSK(IST). The leptokurtic distribution was developed by generating a1C2 value with 1 degree of freedom, which is extremely positivelyskewed. This function routine, RLEP, however, did not generate adistribution as peaked as was expected since only 10,000values were generated. The distributions for each tail turned out to be U-shapedrather than peaked, although tha measure of waslarger than for normal distributions.

From these 12 populations (4 shapes and 3 differentstandard deviations), three additional rransformations were made. The first transformation converted each number obtained fromthe curves to its nearest integer value. This resulted in a distribution of integers which ranged from 0 to 100 inclusive. This transformation is referred to as the "interval" transformation.

As these 10,000 numbers were generated foreach population, a record was made of how manynumbers were observed for each of the Integers 0 to 100. These frequency counts were then used to obtain the percentile rank of each of the integers 0 through100. This yielded a distribution of scores which are equally distributed from a percentile rank of near 0 to a percentile rank of near 100, i.e., a percentile rank was computed for each interval number in each of the 12 populations of numbers. This transformation is referred to as the "percentile" transformation of scores and is rectangular in form. For each of these transformations, other numbers were generated which retained the rectangular shape of the distribution but varied the standard deviations. Since the standard deviation of the percentile distributions was approximately 23.6, each percentile was divided by 3 to obtain an observed standard deviation of approximately 8 and by 6 to obtain an observed standard deviation of approximately 4. The formulas that were used for reducing the standard deviations are Xc = 50 + 1/3(X0 - 50) and Xc = 50 + 1/6(X0 - 50), where Xc is the converted percentile rank and X0 is the original percentile rank.

The third transformation was designed to generate a set of numbers such that the difference between two consecutive numbers was not uniform. The difference between two consecutive numbers follows no set pattern but varies from pair to pair but retains the property of ordering. This transformation is referred to as an "ordinal" transformation and was generated by adding or subtracting randomly selected digits to each of the integers in the first transformation. To obtain the upper half of the distribution, a random number from 1 to 25 was added to 50. Then another random number from 1 to 25 was added to that result, and so on until there were 50 such numbers greater than the starting number of 50. Similarly, random numbers from 1 to 25 were successively subtracted from 50 until 50 such numbers were obtained. At this stage, the numbers varied from -558 to +658 with the distance between numbers varying from 1 to 25 in a random pattern. Although the mean of these numbers, based on the original frequencies, was approximately 50, the standard deviation was much larger than the other transformations, e.g., 182.5.A standard deviation equal to the standard deviations of the other distributions of scores was obtained by standardizing each of the scores and then converting it through stamiatd score transformations to standard deviations of 16, 8 and 4.

The procedure followed to this point produced 36 different populations of scores based on 4 shapes of distributions, three standard deviations, and three types of transformations or scales. For each of the combinations of standard deviations and shapes of distribution, three sets of numbers were stored on computer tape and read into the computer program as needed.These sets of numbers were the interval numbers ranging from 0 to 100, and the corresponding ordinal and percentile transformations for each of the interval numbers. The values describing all of these populations (means, standard deviations, and measures of skew and kurtosis) and frequency distributions for the populations with standard deviation equal to re, are listed in Appendix A.

8 The three sets of numbers so far generated and stored on magnetic tape were used by the main computer program which calculated the r's and t's. The results of this study are based on distributions of r's and t's based on 5,000 "", where an "" is defined as the random selection clf samples of size n for k populations, where n may be 5, 15, or 30, and k may vary from 1 through 12. Different random numbers were generated for each of the 5,000 sets of samples. Thus, the results are based on sampling from an infinite population, each set completely independent of other sets.

For each "experiment", two sets of random numbers were generated by the appropriate subroutine specified for that particular "experiment." The shape, variance, and size of the two samples, hereafter referred to as Sample A and Sample B, were specified for each "experiment", and all sampling distributions of r and t were based on 5,000 sets of random numbers.The procedure used for all "experiments" followed the sequence listed below.

The numbers in each sample were generated by the appropriate shape subroutine -- normal, positively skewed, negatively skewed, or leptokurtic. The size of each sample, n, and the standard deviation for the scores were specified on the control card. As each number was generated, each number was first rounded off to itsclosest integer value. The "ordinal" and "percentile" equivalents to each number generated was then obtained by a "look up" procedure which searched through the score transformations stored on magnetic tape. This table "look up" procedure was done for each interval number in both samples until the specified number of scores had been found. Thus, for an A sample of size 5, there were thus generated 5 interval numbers and the 5 corresponding"ordinal" numbers and the 5 corresponding "percentile" numbers.

After the three sets of numbers for both samples A and B were generated, t's and r's were calculated between all possible combinations of scores for A and B.Thus, a t was calculated between A and B samples when the A scale was interval and the B scale was also interval, when A was interval and B was ordinal, A interval and B percentile, and so on forthe 3 x 3 = 9 combinations of scales for samples A and B. A of the r's and t's was set up for each of the 9 combinations based upon the significance value of the r or t. The values of r or t for each level of significance from .0005 to .9995 for each degree of freedom used in this study were stored in the computer at the outset of the main program. The theoretical t values were obtained from Owen (1962), Bald(1952), and Fedirighi (1959). The theoretical r values were obtained from David(1938) for probabilities equal to or less than .10 and were computed for probabilities of .20, .30, and .40 by using thefollowing formula: t2 r= Al Each computed r or t was then compared to the critical value read into the computer, and a tally made for each r or t equal to or less than the critical value.The resultant cumulative frequencies were divided by 5,000 to obtain the proportion oft's and r's which were equal to or greater than the critical value. The obtained cumulative proportions were then compared to the theoretical distributions of r and t to determine whether or not there was a significant discrepancy. The Kolmorov-Smirnov test was used to determine whether or not there was a significant deviation betweentheoretical and empirical cumulative proportions (Siegel, 1956, pp. 47-52). The .05 level of significance was used for this test and for an N of 5,000, and a difference larger than .0192 was significant at that level.

in reporting the results, the cumulative probabilities were changed to significance levels. Thus for the left tail, the percentages reported are the probability that a t will be equal to or less than that critical value, whereas for the right tail, the percentages reported correspond to the probability that a t is equal to or greater than the critical value. Although the computer provided the obtained cumulative proportions of t and r for the following levels of significance (.0005,.0010, 70050,.0100, .0250, .0500, .1000, .2000, .3000, .4000, .5000), the tables in Appendices B and C list the output only for those values between .0010 and .0500. The reason for this is that these are the probability levels most commonly used forhypothesis testing and listing all values would have made the tables less manageable.

In addition to computing the r's and t's for the nine combinations of scales, the program also calculated the mean, standard deviation, and measures of skewness and kurtosis for each of the three sets of numbers of both the A and B samples. The values for each pair of samples were stored so that after the A and B sampleshad been generated 5,000 times, it was possible to compute the mean of all the A and B means, the mean of all the A and B standard deviations, and the means for the measures of skewness and kurtosis for both A and B. The program also calculated the standard deviation of each of these to determine how varied the setsof samples were. These descriptive statistics were provided as an index of the extent each sample violated certain basic assumptions,namely the shape of each distribution.

The formulas used in this study for the computations of the statistics are as follows:

I X X = N

x2 S. D.= n

m3 Skewness = m2 0171.

m4 - 3 Kurtosis = m2

10 where X denotes a raw score, E x2 denotes the squared deviation about the mean, and m2, m3, and m4 are, respectively, the second, third and fourth moments about the mean. (Ferguson, page 76)

The formulas for r and t are those commonly found in psychological and educational statistics, and are as follows:

NLXY (EX) (EY) r = IN/FT0- x)21[t4 xY2 Y)2]

Ma Mb t = + i x2b + Nb

1413 2 NaNb

11 Results

The results of this Monte Carlo study are listed in tables of the obtained distributions of t's and r's which are presented in Appendices B and C respectively. In order to compPre the results for various combinations of violations, all information relevant to the particular distributions are presented in the same table.

For each table, the proportion of obtained t's or r's exceeding the theoretical values for a one-tailed test at the .001, .005, .01, .025, and .05 levels are given for both tails of the distribution separately. For two tailed tests at a given level, the appropriate proportions can be added together to determine the proportion exceeding the theoretical value for a two-tailed test. The difference between the obtained and the theoretical proportions should reflect the degree to which violations of assumptions affect the distributions of t and r. The theoretical levels of significance for each column are presented across the top of the table.

The types of scales being compared are given in the left column for each sample being compared or correlated. The types of scales used were interval (Int.), ordinal (Ord.), and (Per.). Although in common practice, at least with computing t values, one would not compare means based on different scales, for the purposes of this study comparing various types of scales was done in order to determine the effect on the t distribution for combinations of scales as well as if both samples had the same scale, e.g., an ordinal scale. In practice, there are often situations in which a t test would be used to compare the means of two groups when the type of scale being considered is only ordinal. Thus, the oreemal-ordinal combination would have direct applicability to general usage of the t test. Likewise, there are situations in which the t test might be used to determine whether or not the means for two groups are significantly different when percentile ranks are used. Thus, the percentile-percentile comparisons would have direct applicability. The other combinations of scales may only have theoretical value since one would not compare means based on different types of scales.

The type of distribution and the size of each sample for A then B, are presented in the title of each table. As discussed previously, various combinations of four basic types of distributions were used: normal, positively skewed, negatively skewed, and leptokurtic. The sample sizes for each "experiment" were 5 and 5, 5 and 15, 15 and 15, 15 and 30, and 30 and 30. At the bottom of each table are presented descriptive statistics for each sample. All of these statistics are mean values based on the statistics computed for each of the 5,000 "experiments" used to compute the t and r distributions. The means of the 5,000 means are presented mainly as a check to insure that the means were not deviating from the population mean value of 50. The means of the standard deviations are presented

13 both as a check to make sure that the standard deviations were approximating the values which were predetermined and to serve as a reference for comparing the effect of various sizes of variance. It should be noted that since the formula for computing the standard deviation for each sample was IF x2 , the SD n standard deviations of the samples underestimate the standard deviations of the populations.The measures of skewness and kurtosis are also presented for quick reference as to the type of distributions being compared.

The Kolmogorov-Smirnov goodness-of-fit test was used to determine whether or not the deviations of the obtained distributions were significantly different from the theoretical distributions (Siegel, 1956). The .05 level of significance was used for all comparisons, and the obtained proportions which differed significantly from the theoretical distribution are marked with an asterisk (*).

Since a number of different violations were considered in this study separately and in combination, the results will be presented in a series of tables in which the various types of populations are grouped together with subgroupings of tables with variations in variances and types of scales. The combinations of variances and types of scales for samples from normal population distributions will be considered first, i.e., both Sample A and Sample E are from normal populations of scores. Next will be considered the results of sampling from populations in which Sample A is from a normal distribution and Sample B is from a skewed distribution. The third grouping of tables will present the results for situations in which both the samples are from non-normal distributions but both samples are from the same type of distribution. In this grouping will be considered the results of sampling from two positively skewed distributions. The next two groupings will present the results for sampling from non-normal distributionsin which the two samples are from two different kinds of populations. The fourth grouping will consider sampling from a positivelyskewed distribution for Sample A and from a negatively skewed distribution for Sample B. The fifth grouping will present the results for samplings from skewed and leptokurtic distributions.

For each of the five major subgroupings of scales as delineated above, two subgroupings of scales will be considered for each. The first is for those "experiments" in which the size of the sample is the same for both Sample A and Sample B. The second is for those "experiments" in which the size of the sample is different for each sample. For each of these two subgroupings, the following subgroupings will be considered. The first will be for those samples in which both the A and B variances are comparableand the same types of scales are being considered. The second will be for samples with again equal variances but for different types of scale. The third and fourth groupings will be for samples in which thevariances are different for each but for the first group thescales are the same for the second group the scales aredifferent. It should be

14 remembered that the percentile rank transformation is a rectangular distribution, thus making a combination of variation in both shape of distribution and type of scale.

In outline form, the tables will be discussed in the following sequence for each of the six major groupings based on basic types of distributions: A. Equal sample sizes. 1. Variances equal, same type of scales. 2. Variances equal, different types of scales. 3. Variances unequal, same type of scales. 4. Variances unequal, different types of scales. B. Unequal sample sizes. 1. Variances equal, same type of scale. 2. Variances equal, different types of scales. 3. Variances unequal, same type of scales. 4. Variances unequal, different types of scales. Distributions of t forSamples from Normal Distributions

The proportions of t values obtained for the sampling distributions from samples from normally distributed populations are presented in Tables B-1 through B-19. The first seven tables are for those situations in which the same size of sample is used for both A and B.

For the situation in which there are no differences between sample A and B with regard to shape, size, variance, and type of scale, the obtained distributions follow very closely to the theoretical distribution. The obtained distributions of t remain fairly close to the theoretical distribution even for the situation in which the size and variance of the tv'' samples is the same but the type of scale is changed from interval to ordinal. This holds for the situation in which both scales are changed from interval to ordinal and for the situation in which the scale is changed for only one sample, i.e., an ordinal and interval combination of scales.

For the samples in which there is a difference in variance, and the same scales are being considered, the obtained distribution of t is also close to the theoretical distribution. This is true even for the situation in which n = 5 for both samples and the ratio of one variance to the other is 1 to 16, i.e., a population standard deviation of 4 for Sample A and 16 for Sample B. However, when unequal variances and type of scale are combined, at least for those comparisons involving the percentile transformation, there are significant discrepancies between obtained and theoretical distributions of t. Generally, there is a larger proportion of t's than expected and the distribution of t's is sliphtly skewed with the direction of skew in the direction of the sample with the larger variance.This is true for the situation in which the population standard deviations are 4 and 28. As the differences in standard deviations of the populations from which the samples are drawn are reduced, the discrepancy between theoretical and obtained distributions of t is also reduced. For the situation in which the standard deviations are approximately the same, the obtained t distribution follows the theoretical distribution very closely.

Thus, it seems that when sampling from normal distributions and when the samples are the same size, only extreme differences in variances have an effect on the obtained distribution of t. It also seems as though the discrepancy is caused by differences in variance rather than the type of scale being considered, since the discrepancy is not significant when the difference in variances of the two samples is reduced and two different types of scales are used for Sample A and Sample B.

Also, it can be noted from Tables B-5 through B -7 that with larger sample sizes, e.g., n = 15 or 30, there are no significant discrepancies between obtained and theoretical distributions even with combinations of differences in variances and types of scales.

17 Tables B-8 through B-19 present the results for the samples with unequal n's. Adding the variable of differences in sample size drastically affects the observed distributions of t when there is a combination of differences in variance and types of scale. For the situation in which the variances of the two samples are equal and the same type of scale is useJ, theobtained distribution of t is close to the theoretical distribution. This is also true for comparisons involving a change in scale, i.e., interval to ordinal. As long as the variances remain equal, a change of scale from interval to ordinal does not affect the t distribution even for samples with unequal n's. However, for the percentile transformations which also involve a change in shape of oistribution, there are significant discrepancies between obtained and theoretical distributions even when the variances are equivalent. As can be noted in Tables B-10 and B-13, the comparisons of both interval and ordinal scores with percentile scores results in asignificantly greater proportion of t's when the larger variance is associated with the larger sample size, and the proportion tends to be slightly less when the reverse is true.

The obtained distributions of t depart quite drastically from the theoretical distributions for the "experiments" in which the same types of scales were considered but forwhich the sizes and variances differed. The results are similar for both the interval and ordinal scales and for the combinations of these scales.With standard deviations of 4 for the smaller sample and 16 for thelarger sample, the proportion of t's obtained is much smaller than expected, e.g., as listed in Table B-12, .0042 for a two-tailed testin which both scales are interval compared to the theoretical .05 level.When the sample with the smaller size has the larger standard deviation, the proportion of t's obtained is much greater than expected, e.g., as listed in Table B-17, .1492 for a two-tailed testin which both scales are interval compared to the theoretical .05 level. At the .01 level, .0586 exceed the nominal value.The results are similar for the "experiments" in which the differences in population variance is on a ratio of 1 to 4, i.e., a standard deviation of4 for one sample and 8 for the other sample. From an examination of these tables, it becomes apparent that the combination of differences in sample size and differences in variance is associated with significant departures of the obtained distribution of t from the theoretical distribution. The same results remain even when the sample sizes are increased to 15 and 30, and are similar to the findings of Boneau(1959) and Welch (1937).

For the comparisons in which the percentile transformations are involved, the results are similar tothose above. However, it seems as though the discrepancy between obtained andtheoretical t distributions is more a function of the combination of differences in variances and sample sizes than it is in type of scale. Considering the situation in which an interval scale is used for Sample Aand the percentile transformation is used for Sample B, when thesample sizes and standard deviations are, respectively, n = 5, SD =4 and

18 n = 15. SD = 28, there are wide discrenancies between theoretical and obtained distributions of t. As an example, in Table B-8 the proportion of t's exceeding the nominal .05 level for a two-tailed test is only .0042. In Table B-10, where the standard deviations are equivalent, the proportion of t's exceeding the nominal . 05 level is .0346, and in Table B-14 for the same comparison, . 0402 exceed the liominal .05 level when the standard deviations are 4 and 4. Thus it seems that the discrepancy is associated more with difference in veriance than with type of scale and in this case shape of distribution.

Many other combinations of the variables listed in these tables could be considered.A lengthier discussion of these tables would point out the results of specific combinations of violations. However, the examples cited above seem to point out the general effects of these combinations of violations.

It should be pointed out that the results for sampling from combinations of normal and leptokurtic populations as well as when both populations were leptokurtic are almost identical to the results of sampling from normal populations. Thus, the results presented in tables B-56 through B-67 and B-130 through B -136 are very similar to the results in tables B-1 through B-19. Possibly this was due to the fact that the shapes of the leptokurtic distributions were not as peaked as they might have been, but more likely this was due to the fact that for small samples the samples are quite platykurtic. The means of 5,000 individual measures of kurtosis for samples where n = 5 hovers around -1.0 for both the samples from normal and leptokurtic distributions. Even when n is increased to 15, the mean of the measures of kurtosis is only around +1.0 for the interval scales and slightly less than that for the ordinal scales. Thus, the samples from normal and leptokurtic populations are very similar with regard to kurtosis and skewness, and the results of this study for sampling from normal populations seem to apply to sampling from leptokurtic populations or combinations of normal and leptokurtic populations as long as both of the distributions are symetrical. As will be poi-.ted out later, the results for combinations of leptokurtic and skewed populations are different than for combinations of normal populations and skewed populations. Distributions of t for Samples from normal and Skewed Distributions

The proportions of t values computed between samples from normally distributed and skewed populations are presented in Tables B-20 through B-55. Since the results are i.ientical but reversed for the positively skewed as compared to the skewed populations, the discussion will deal only with the sampling distributions of t for samples from normal and positively -kewed populations. These results are presented in Tables B-20 Occough B-41.

For the "experiments" in which Sample A is from a normally distributed population and Sample B is from a skewed population and when the sizes of the samples, variances, and types of scales for the two samples are the same, there are significant discrepancies between the obtained and theoretical distribution of t, at least when the sample size is 5 for both samples.There is a consistent trend for the distribution of t's to be skewed in the direction of the skew in the population from which samples are drawn. This trend prevails even when the size of the sample is increased to 15, although the discrepancies are not significant with this larger sample size.

This trend continues regardless of the type of scale used if the other variables remain constant. In fact, a change of scale from interval to ordinal or percentile rank seems to reduce the discrepancy between observed and theoretical distributions of t. Possibly this might be due to the fact that the average skew for ordinal and percentile rank transformations is not as large as for the interval scales.

The distribution of t becomes quite skewed for samples with unequal variances even when the sample size is 30 for both samples. For the situation in which the scales are the same for both samples and the differences in the population variances are 16 and 64, as for example in Tables B-23 and B-24, the proportion of t's exceeding the nominal 5 per cent level on a one-tailed test is approximately .11 for the right tail and stays around .02 in the left tail.

Similar results are noted when a change in type of scales is added. As with other combinations of scales discussed so far, the discrepancies in the t distributions are similar for both the interval and ordinal scales. However, more of the percentile transformations are now involved in the significant discrepancies. Possibly this might be due to the fact that regardless of scale, when small samples are drawn from skewed populations, there are more samples with means less than Or greater than in the case of negatively skewed distributions) the population mean even though the mean for all means is equal to the population mean. Since the greater proportion of scores in a skewed distribution are located in the tail opposite the skew, it seems reasonable to assume that most of the scores will be randomly drawn

21 from this area. Thus, the distribution of t for skewed distributions would also be skewed in the same direction as the skew in the population, dependent of course on which mean is subtracted from the other in the numerator.

For the situations in which the n's are not equal, there are significant discrepancies between obtained andtheoretical distributions of t even when the variances and types of scale are the same for both samples. Again, as can be observed in the tables beginning with Table B-30, the distribution of t is skewed in thedirection of the skew in the population. This is true and remains consistent regardless of the type of scale which is being considered. However, the discrepancy is slightly less when one or both of the scales is the ordinal transformation. Possibly this is because the ordinal transformations are less skewed than the interval scales. The comparisons involving the percentile rank transformations result in as many or more significant discrepancies than the comparisonsinvolving only the interval scales. Possibly this might be due to the slightly higher standard deviation of the percentile rank samples than the samples using the interval scales. As can be seen in Table B-32, when the smaller standard deviation is associated with the smaller sample size the proportion of t's is less than the ex; -acted theoretical proportion and more than expected when the combination is reversed. This seems to be happening even when the difference in standard deviations is less than one point.Possibly there is a compounding of effects of shapes of distributionand different variances. However, for the interval-percentile and the ordinal- percentile scale combinations the higher proportion ofis is in the left tail rather than the right tail. This might be an indication that differences in variances has more influence on the proportion of obtained t's than shape of distribution.

Larger differences in variances between the two samples drastically affects the proportion of obtained t's. Referring to Table B -34, the proportions of observed t's diminishes to almostnothing in the tail opposite the skew for combinations of both smallersample size and the smaller variance. At the nominal .025 level for a one- tailed test, only .0004 of the t's exceed the t value at thislevel. The proportion of t's exceeding the same level for the righttail is only .0138. The above is for the situation in which the ratio of the variances is 1 to 16 and both scales are interval. When the ratio of the variances is reduced to 1 to 4, i.e., standard deviations of 4 and 8, the pattern remains almost the same for theleft tail but the proportion of t's for the right tail increases andapproaches the .05 proportion of t's at the nominal 5 per cent level for aone-tailed test. This same pattern holds regardless of the type of scalesbeing considered, and is consistent even when the sample sizes areincreased to 15 and 30.

When the sample with the smaller variance has thelarger n, as in Tables 8-38 through B-41, there is aconfounding effect of the

22 variance-size phenomena and the shape-of-distribtuionphenomenon. Here the obtained proportions greatlyexceed the theoretical proportions in both tails.This is true even for small differences in standard deviation, e.g., 4 and 6 aslisted in Table B-40 . for the percentile-interval comparisons,and for samples sizes of 30 and 15 as listed in Table B-41. Thus it seems as though the combination of samples from normal and skewedpopulations tends to influence the distribution of t when the othervariables are equal and has a very pronounced effect when thevariances and size of samples are different for each set of samples.

23 e?6 Welch, B. L. The generalization of student's problem when several different population variances are involved. Biometrika, 1947, 34, 28-35.

39 Distributions of t for Samples from Positively SkewedDistributions

The distribution of t values computed between samplescoming from positively skewed distributionsare presented in Tables B-68 through B-89. Tables B-68 through B-77 present the results for the comparisons involving the same sample sizes, and Tables B-78 through B-89 present the results for comparingsamples of uneaual sizes.

Under the conditions of equal variances, equal n's, and same type of scale, the obtained distribution of t is fairly close to the theoretical distribution. This is true for all three types of scales separately or in combination. Thus, sampling from distributions which are skewed in the same direction doesnot have a significant effect on the t distribution provided the size of thesamples and their variances do not differ regardless of thetype of scale.

For the same conditions as listed above but with the exception that there is a significant difference in the variances of the two samples, the distribution of obtained t's is significantly different than the theoretical distribution. For the "experiments" in which both samples sizes are n= 5, the distribution of t's is skewed in the direction of the skew of the population. For all three types of scales either separately or in combination, thetrend is for the proportion of t's to be greater than expected in the right or positive tail, and less than what would be expected in the left tail. The trend remains very consistent from samples ofn = 5 each to n = 30 each. Thus, increasing the size of the samples does not reduce the discrepancy as muchas in some previous "experiments". There is some variation in the extent of discrepancy as the ratios of the standard deviations become closer, For the ratio of variances of 1 to 16, as in Table B-70, the proportion of t's which exceed the nominal 5 per cent levelon a one-tailed test are .0236 and .1422 for, respectively, the left and right tails of the t distribution. When the ratio of variances is 1 to 4 as in Table B-71, the proportions for the same comparisonsare .0294 and .1048. For this same variance ratio, i.e., 1 to 4, increasing the size of both samples to 30 changes the proportion of t's to, respectively, .0326 and .0748 as presented in Table B-77.

It is interesting to note that for most of these comparisons the larger variance was for Sample B. Since the numerator of the t formula used - t, possibly the larger proportion of t's in the right tail is due to the fact that most of the B means were lesi than the A means because of the larger variance. However, for the interval- ordinal comparisons in which the larger variance is also in Sample B, the proportion of t's is larger in the left tail.This trend is more prevalent when the variances are equal. Possibly there is a effect of differences in variances and shapes of distributions.

For the experiments in which the n's of the two samples differ, there is a slight trend for the t's to be positively skewed when the variances of the two samples are equal. This seems to be true for the interval and ordinal scales, but for the interval-percentile and ordinal-

25 .,.

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APPENDIX A

POPULATION VALUES AND DISTRIBUTIONS percentile combinations of scales just the reverse is true. A comparison of the distribution of t's for these combinations of scales as presented in Tables B-80 and B-81 shows that there are significant discrepancies in the t distribution even with very slight differences in variance.When the A sample has the interval scale and the smaller standard deviation, 3.2 compared to 4.6, the proportion of t's in the right tail is less than expected. When the A sample has the percentile scale and the standard deviation of 4, the proportion of t's is greater than expected. This again might be indicative of the greater influence on the t distribution due to differences in variance rather than shape of distribution.

For the combinations of differences in n and variance for the two samples, large discrepancies between obtained and theoretical distributions of t are found.As in previous examples, when the sample with the smaller n has the smaller variance, the proportion of t's is significantly less than expected. This is especially true for the left tail, or in this case, the tail opposite the skew in the population of scores. This tendency is true for all scales and for n's of 5 and 15 and 15 and 30. When the sample with the smaller variance is larger in size, the proportion of t's is larger than expected and the distribution of t's is positively skewed. This is true for both the interval and ordinal scales used and for combinations of n's ranging from 15 and 5. to 30 and 15. These results are similar to the results of sampling from normal and skewed distributions. Table A-1

POPULATION VALUES FOR DISTRIBUTIONS WITH STANDARD DEVIATION OF 16, N = 10,000

Shape of Type of Standard Distribution . Scale Mean Deviation Skewness Kurtosis

Interval 50.268 16.197 0.010 -0.173

Normal Ordinal 50.000 16.000 0.016 0.114

Percentile 50.000 28.862 0.000 -1.200

Interval 49.704 15.970 0.917 0.223 Positive Skew Ordinal 50.000 16.000 1.039 0.631

Percentile 50.000 28.860 0.001 -1.201

Interval 50.722 16.151 -0.971 0.380 Negative Skew Ordinal 50.000 16.000 -1.090 0.803

Percentile 50.000 28.860 -0.001 -1.201

Interval 50.173 14.292 -0.004 0.773

Leptokurtic Ordinal 50.000 16.000 0.002 1.661

Percentile 50.000 28.834 -0.001 -1.213

A-1 Distributions of t for Samples from Positive and Negative Skewed Distributions

When t's are computed between two samples which are skewed in opposite directions, the distributions of such t's are usually significantly different from the theoretical distribution and are generally skewed. The results for these comparisons are presented in Table B-90 through B-115.

For the "experiments" in which the n's, variances, and types of scales used are the same for both samples and the only difference is the opposite skew in the population distributions, the distributions of t's are skewed and deviate significantly from the theoretical distributions. This is true for all scales, with the exception of when both samples use percentile scales. However, for those comparisons in which one of the samples usesan ordinal or interval scale and the other sample uses a percentile scale, the discrepancy is not quite as large and is usually not significant. .Possibly this is due to the fact that the percentile transformations are not as skewed as the other two types of scales. Increasing the sample size from 5 and 5 to 15 and 15 reduces the extent of the discrepancy but most of the discrepancies are still significantly different from the theoretical distribution. There is a further reduction when the size of the samples is increased to 30, with fewer of the discrepancies significantly different from the theoretical distribution.

When there is a difference in the variance between the two samples from oppositely skewed distributions, the discrepancy between obtained and theoretical increases but not to the same extent than changes in variance affected other t distributions. Possibly this might indicate that the discrepancy is due more to the shape of the distributions and differences in variances do not confound the results as much as with other shapes of distributions.

It should be noted again that the numerator of the t formula consistently used A - B. Since the A samples were from positively skewed distributions for all comparisons and the B samples were from negatively skewed distributions, the obtained t distributions were positively skewed with most of the t's in the left tail. This is probably due to the fact that the majority of the A means were probably lower than the population mean for A, whereas the majority of the B means were probably higher than the population mean for B. Thus, most of the differences between means were negative thus resulting in more negative t values. In order to determine if this was happening, Table B-90 was re-run but with the negatively skewed distribution for Sample A. The results were identically opposite the results in Table B-90. Thus, the direction of the skew in the distribution of t is due to the probability of obtaining more means from the larger area of skewed distributions and the direction of the skew will depend upon which mean is subtracted from the other.

With unequal size samples but with the variances equal, the distributions of t follow the same pattern as above, i.e., significant

27 ,(0 Table A-2

POPULATION VALUES FOR DISTRIBUTIONS WITH STANDARD DEVIATION OF 8, N = 10,000

Shape of Type of Standard Distribution Scale Mean Deviation Skewness Kurtosis

Interval 50.102 8.023 -0.009 0.039

Normal Ordinal 50.000 8.000 -0.012 -0.224

Percentile 50.000 28.846 0.000 -1.999

Interval 49.851 7.914 1.589 3.457 Positive Skew Ordinal 50.000 8.002 1.573 3.600

Percentile 50.000 28.825 0.005 -1.204

Interval 49.956 8.053 -1.565 3.199 Negative Skew Ordinal 50.000 8.001 -1.545 3.279

Percentile 50.000 28.827 -0.005 -1.204

Interval 49.969 8.919 -0.064 5.067

Leptokurtic Ordinal 50.000 8.001 -0.058 4.650

Percentile 50.000 28.797 -0.001 -1.219

A-2 discrepancies from theoretical and skewed to the left. This is generally true for all scales.However, for the t distributions involving percentile scales the discrepancy is usually not as large and sometimes is even skewed in the opposite direction. Possibly this is again due to the fact that the percentile transformations were not as skewed as the interval and ordinal transformations, or, possibly the slight difference in standard deviations might be causing this effect. That this might be suspected comes from looking at Table B-106, comparing the interval-percentile and percentile- interval pairing of scales and standard deviations. It seems as though the size-of-sample matched to size-of-variance phenomenon might be producing this effect here as it has in numerous other examples, even though there is less than one point differences in the standard deviations.

When unequal sample size is combined with unequal variances the same phenomenon seems to influence the distribution of t as it has with other shapes of distributions. The t distribution remains positively skewed with most of the t values in the left tail.As with other combinations of sizes of variance and sample size, t distributions based on samples with the combination of small size and small variance are significantly less than what would be expected. The fact that the t distributions are skewed seems to indicate that there is a confounding effect of the influence of size and variance plus the fact that the samples are drawn from skewed distributions. When the ratio of variances is 1 to 4 for, respectively, the samples with n = 5 and n = 15, the proportion of t's exceeding the nominal 5 per cent level in the left tail is about .04 but for the right tail is only .007. When the size of the samples is reversed, the proportions of t's are, respectively, .1780 and .0860. This trend is the same even for the samples with n = 30 and n = 15.

28 Table A-3

POPULATION VALUES FOR DISTRIBUTIONS WITH STANDARD DEVIATION OF 4, N = 10,000

Shape of Type of Standard Distribution Scale Mean Deviation Skewness Kurtosis

Interval 50.071 4.004 0.015 -0.309

Normal Ordinal 50.000 4.004 -0.040 -0.606

Percentile 50.000 28.785 0.000 -1.196

Interval 49.971 4.021 1.720 4.256 Positive Skew Ordinal 50.000 4.000 0.995 0.528

Percentile 50.000 28.702 0.019 -1.212

Interval 50.034 4.079 -1.711 3.976 Negative Skew Ordinal 50.000 3.997 -0.966 0.176

Percentile 50.000 28.699 -0.019 -1.210

Interval 50.048 3.908 -0.043 10.646

Leptokurtic Ordinal 50.000 4.002 -0.091 5.156

Percentile 50.000 28.642 -0.002 -1.234 Distributions of t for Samples from PositivelySkewed and Leptokurtic Distributions

The distributions of t obtained from comparingsamples drawn at random from skewed and leptokurticdistributions are presented in Tables B-116 through B-129. Again, since the effects are just reversed for the negativelyskewed compared to the positively skewed distributions,only the results comparing the positively skewed with the leptokurticdistributions will be discussed. These results are presented in Tables B-116 through B-122.

For the "experiments" in which the sizes of thesamples and the variances are equal, there isa slight skew in the obtained t distribution, with the higher proportion in the tailopposite the direction of the skew for the populationdistribution. However, the effect is not very extensive resulting in .0734and .0270 t's falling in, respectively, the left and right tailsat the .05 level for a one-tailed test. The result is similar for sample sizes of 15 for each sample compared ton = 5 as reported above. When the scale used is ordinal for bothor either one of the samples, the distributions of obtained t's is closerto the theoretical distribution. With equal n's but with differences in variances between the two samples, the obtained distributionsof t are very close to the theoretical distributioneven when the ratio of one variance to the other is 1 to 16. This is true for both the interval and ordinal scales. However, for the distributions of t values obtained when there is a combination ofdifferences in variance and the two scales being comparedare either interval and ordinal compared to percentile, thereare significant discrepancies between obtained and theoretical distributions oft. For the smaller size samples, n = 5, there are significantly greaterproportions of t's in both tails of the distributionsthan one would expect. For n = 15, the proportion of t's in both tails tends to be slightly but not significantly greater, e.g., .0572 and .0558at the .05 level for one-tailed tests.

For samples with unequal n's, there are not significant discrepancies between obtained and theoreticalt distributions for the interval and ordinal scales when the variancesof the two samples are equal. For all scales, either separately or in combinations, when there are differences between thetwo samples with regard to both sample size and variance, thereare significant discrepancies between the obtained and the theoretical distributions oft. The proportions follow the same patternas with other shapes of distributions, namely that when the sample with the smallervariance also has the smaller n, the proportion of t's obtained is much less thanexpected, e.g., .0032 for a two-tailed test at the nominal .05 level. For the reverse combination of size and variance, the proportion if much larger than expected, e.g., .2628 fora two-tailed test at the nominal .05 level.

29 NORMAL DISTRIBUTION STANDARD DEVIATION =16N=109000 INT PER ORD "FRE() 0 0.005 -2.87383 1.000 1 0.015 -1.57597 1.000 2 0.055 -0.53768 7.000 3 0.100 0.06798 2.000 4 0.120 0.67365 2.000 5 0.140 1.79847 2.000 6/0.175 3.61547 5.000 7 0.220 3.96157 4.000 8' 0.285 5.60553 9.000 9! 0.385 6.73034 11.000 10 0.515 8.54735 15.000 11 0.635 9.15301 9.000 12 0.785 10.01826 21.000 13 0.955 11.92179 13.000 14 1.145 13.04660 25.000 15 1.455 14.17141 37.000 16 1.780 15.90189 28.000 17 2.075 17.19975 31.000 18 2.345 17.63238 23.000 19 2.705 18.23804 49.000 20 3.140 19.18981 38.000 21 3.580 20.66072 50.000 22 4.135 21.09334 61.000 23 4.815 22.65077 75.000 24 5.520 24.81387 66.000 25 6.230 25.07345 76.000 26 6.985 25.59259 75.000 27 7.755 27.32307 79.000 28 8.625 27.66917 95.000 29 9.620 29.48618 104.000 30 10.650 30.52447 102.000 31 11.810 31.73580 130.000 12 13.095 32.25495 127.000 33 14.435 33.55281 14,1.000 34 15.815 34.85067 135.000 35 17.310 35.54286 164.000 36 19.035 36.75420 181.000 37 20.900 38.22511 192.000 38 22.720 39.00383 172.000 39 24.570 41.16693 198.000 40 26.515 41.59955 191.000 41 28.575 41.77260 221.000 42 30.720 42.37827 208.000 43 32.920 42.4,6479 232.000 44 35.110 42.63784 206.000 45 37.300 43.24351 232.000 46 39.635 44.10875 235.000 47 42.145 44.88746 267.000 48 44.760 46.96404 256.000 49 47.155 48.86757 223.000

A-4 1' Distributions of r for all Populations

For all of the "experiments" involving an equalnumber of scores for each sample and standard deviations of4 and 16, correlation coefficients were computed between the two samples of scores. A total of 324 distributions of r's were computed, 108 of which are presented in Appendix C. Since the r was not influenced to the extent that t was, it was deemed not necessary to present all of the tables but to present thosetables for the comparisons involving situations in which no violations were made to exist to situations in which extreme violationsof the assumptions existed.

The results of comparing the obtained distributionsof r to the theoretical distributions indicatedthat there were minor discrepancies under all conditions studied. The distributions of r for situations in which no violationsin shape of distribution are known are presented in Table C-1. Under these conditions the obtained distributions are very close to thetheoretical distributions even when interval or ordinal scales arematched with percentile ranks and the standard deviations are,respectively, 4 and 24. The results for other normal distributions presented in the next three tables, C-2 through C-4, also indicatethat regardless of ratios of variances or types of scales, the obtained distributions are close to their respectivetheoretical distributions.

When the samples are drawn from normallydistributed and positively skewed distributions, the distributionsof r are still very close to the theoretical distributions. The results of these computations are presented in Tables C-5through C-8. Regardless of type of scale or ratio of variances, even for n = 5 the distributions of r are veryclose to their respective theoretical distributions.

For the "experiments" in which one sample wasdrawn from a positively skewed populationof scores and the other was drawn from a negatively skewed distribution, there is aslight skew in the obtained distributions of r, but there is only oneinstance where the proportion of r's is significantly differentfrom theoretical. This is in Table C-11, and is the only significantdiscrepancy for all 324 distributions of r's computed in the study. As indicated above, for all distributions of r computed betweenoppositely skewed distributions of scores, there was a tendency forthe distributions of r to also be skewed, and this tendency seems tobe more pronounced for n = 15 than for n = 5. Possibly this might be due to the fact that the larger sized samples were more skewed thanthe smaller samples. The average measure of skew for n = 5 was around + or 7.4 whereas for n = 15 the average skew was around + or -1.0. For sample size n = 5, the discrepancy between observedand theoretical proportions is generally within + or - .01 of the nominal .05level but is much 50 49.455 49.73281 237000 51 51.815 5059805 235.000 52 54.305 52.50158 263.000 53 56.895 54.57816 255.000 54 59.390 5535688 244.000 55 61.825 56.22212 243.000 56 64.055 56.82779 203.000 57 66.170 57.00084 220000 58 68.295 57.08736 205.000 59 70.360 57.69303 208.000 60 72.440 57.86608 208.000 61 74.440 5829870 192.000 62 76.240 60.46180 168.000 63 77.925 61.24052 169.000 64 79.670 62.71143 180.000 65 81.355 63.92276 157.000 66 82.950 64.61496 162.000 67 84.475 65.91282 143.000 68 85.795 67.21068 121.000 69 87.050 67.72983 130.000 70 88,405 68.94116 141.000 71 89.760 69.97945 130.000 72 90.860 71.79646 90.000 73 91.795 7214255 97.000 74 92.685 73.87304 81.000 75 93.525 74.39218 87.000 76 94.305 74.65175 69.000 77 95.000 76.81485 70.000 78 95.660 78.37229 62.000 79 96.240 78.80491 54.000 80 96.715 80.27582 41000 81 97.150 81.22758 46.000 82 97.545 8183325 33.000 83 97.870 82.26587 32.000 84 98.175 83.56373 29.000 85 98.430 85.29422 22.000 86 98.655 86.41903 23.000 87 98.855 87.54384 17.000 88 99.005 89.44737 13.000 89 99.170 90.31261 20.000 90 99.345 90.91828 15.000 91 99.455 92.73529 7.000 92 99.540 9386010 10.000 93 99.640 95.50406 10.000 94 99.715 9585015 5.000 95 99.785 97.66716 9.000 96 99.845 98.79197 3.000 97 99.870 99.39764 2.000 98 99.895100.00331 3.000 99 99.950101.04160 8.000 100 99.995102.33946 1.000

A-5 .16 closer for higher levels of probability. This is true for all combinations of scales and ratios of variance. The proportions or r in Tables C-9 through C-12 represent the distributions if r which were computed under more violations of the basic assumptions than the situations in other computations.Even 'though the discrepancy between obtained and theoretical distributions of r was largest for these computations, the fit is very good. Thus, it could be concluded that even under extreme violations of the basic assumptions underlying r there is little effect on the obtained distributions of r. POSITIVE SKEW STANDARDDEVIATION =16N=109000 INT PER ORD FRED

0 O. - 3.37754 0. 0. - 2.06052 O. 2 0. 1.00691 0. 3 0. -0.39230 O. 4 O. 0.22231 O. 5 O. 1.36372 O. 6 O. 3.20754 0. 7' 0. 3.55875 O. 8 O. 5.22697 O. 9 0. 6.36838 O. 10 0. 8.21221 0. 11 0. 8.82681 0. 12 0. 9.70482 0. 13 0. 11.63645 0. 14 0. 12.77786 O. 15 0. 13.91928 0. 16 0. 15.67530 O. 17 0. 16.99231 0. 18 O. 17.43132 O. 19 O. 18.04593 O. 20 O. 19.01174 0. 21 O. 20.50436 0. 22 O. 20.94336 0. 23 O. 22.52378 O. 24 0. 24.71881 O. 25 0. 24.98221 O. 26 O. 25.50902 O. 27 O. 27.26504 0. ?8 0.630 27.61625 126.000 29 2.170 29.46007 182.000 30 4.295 30.51368 243.000 31 6.615 31.74290 221.000 32 9.200 32.26970 296.000 33 12.250 33.58672 314.000 34 15.330 34.90374 302.000 35 18.325 35.60614 297.000 36 21.465 36.83536 331.000 37 24.600 38.32798 296.000 38 27.665 39.11819 317.000 19 30.725 41.31322 295.000 40 33.730 41.75222 306.000 41 36.645 41.92782 277.000 42 39.340 42.54243 262.000 43 42.015 42.63023 273.000 44 44.735 42.80583 271.000 45 47.360 43.42044 254.000 46 49.875 44.29845 249.000 47 52285 45.08866233.000 48 54.775 47.19589 255.000 49 57.100 49.12751 220.000

A-6 Summary and Conclusions

In order to assess theeffects of violations of thebasic assumptions underlying r and t, atotal of 1,332 distributions of these t and 324 distributionsof r were obtained by computing statistics between samples which wereknown to violate the basic assumptions in various degrees. Various combinations of differences in shape of distribution,variance, size of sample, and type The general paradigm which wasfollowed in of scale were studied. of either this study was, given a truenull hypothesis, the proportion the r's or the t's exceedingthe nominal levels of significance should reflect the influence ofthe violation or combinationof Thus, the proportion of obtainedr's or t's exceeding violations. when the values of these statisticsfor a given significance level the null hypothesis is true and allassumptions are met should indicate whether or not a particularviolation had an influence on the obtaineddistributions and to what extent.

The results of this study indicatethat the Pearson product rather extreme moment correlationcoefficient is insensitive to violations of the basic assumptions. Failure to meet the basic assumptions separately or invarious combinations had littleeffect distributions, on the obtaineddistributions of r. For all of the 324 each of which was based on5,000 r's, there was only oneproportion of r's which deviated significantlyfrom the nominal expected tailed test proportion. This was at the .05 level for a one involving correlation coefficientscomputed between samples one of which came from a positivelyskewed distribution and the other from a negatively skeweddistribution. Thus it is concluded that the effect of the basicassumptions underlying r is negligible.

The results of this study aresimilar to the results of the study by Norris andHjelm (1960). These authors found of that when the populationcorrelation was near zero, the shape the sampling distributions of rdid not vary markedly as a Also, function of nonnormality in thedistributions of scores. when sampling from skeweddistributions, the sampling distributions distribution of of r was also slightlyskewed causing one tail of the r to have a higher proportion ofr's than expected and the other However, this author tail a smaller proportion ofr's than expected. does not feel that the discrepancybetween observed and theoretical proportions is great enough to causethe researcher to not use r when violations of the basicassumptions are known to exist. Possibly, as pointed out by Lindquist(1953, p. 81), one should of make allowances for thesediscrepancies in the interpretation the results the results of one's study. For example, referring to presented in Table C-12, when thenominal risk of a Type I error risk may is .01 for a one-tailed testthat r is negative, the true positive, the true risk be as large as .02'. For the test that r is may be only as large as.005.

33 50 59.175 50.00552 195.000 51 61.260 5088353 222.000 52 63.340 52.81 516 194.000 53 65.320 54.92238 202.000 54 67.175 55.71259 /69.000 55 68.935 56.59060 183.000 56 70.800 57.20521 190.000 57 72.460 57.38081 142.000 58 73.925 57.46862 151.000 59 75.315 58.08322 127.000 60 76.580 58.25882 126.000 61 77.865 58.69783 131.000 62 79.145 60.89286 125.000 63 80.445 6168307 135.000 64 81.640 6317569 104.000 65 82.725 64.40490 113.000 66 83.715 65.10731 85.000 67 84.655 6642433 103.000 68 85.655 67.74134 97000 69 86.590 68.26815 90.000 70 87.445 69.49736 81.000 71 88.210 70.55098 72.000 72 88.860 72.39480 58.000 73 89.510 7274600 72.000 74 90.260 74.50203 78.000 75 90.965 7502883 63.000 76 91.540 75.29224 52.000 77 92.045 77.48726 49.000 78 92.600 79.06768 62.000 79 93.205 79.50669 59.000 80 93.775 8099931 55.000 81 94.325 81.96512 55000 82 94.780 8257973 36.000 83 95.175 8301873 43.000 84 95.660 84.33575 54.000 85 96.140 86.09177 42.000 86 96.560 8723318 42.000 87 96.935 88.37460 33.000 88 97.265 90.30622 33.000 89 97.570 91.18423 28.000 90 97.825 91.79884 23.000 91 98.080 9364266 28.000 92 98.350 94.78408 26.000 93 98.615 96 45230 27.000 94 98.855 96.80350 21.000 95 99.095 98.64733 27.000 96 99.325 99.78874 19.000 97 99.48010040335 12.000 98 99.64010101795 20.000 99 99.805102.07157 13.000 100 99.935103.38858 13.000

A-7 The results of this study seem to indicate that the t test is not as robust as other researchers have found, e.g., Boneau (1960) and the Norton study (Lindquist, 1953). However, the results are consistent with those of Baker et al (1966) who found that the t distribution is little affected by the type of measurement scale used.

The results of this study are summarized in Table 1 which gives for selected combinations of shape of population, variance, and sample size the proportion of obtained t's falling outside the nominal .05 and .01 probability limits for one-tailed tests in both directions. The combinations are representative of those used throughout the study and are for combinations of normally distributed, positively skewed, negatively skewed, and leptokurtic distributions. However, since type of scale did not seem to influence the obtained distributions of t, only the results for combinations of samples in which both samples used the interval transformations were considered for this summary table. For comparative purposes, the format of the table is similar to the table prepared by Boneau (1960, p. 61).

The results of this study lead to the following conclusions:

1. When sampling from normal distributions, the obtained distribution of t's matches the theoretical distribution when either or both the n's or variances are equal for both samples. However, when there are differences with regard to both variance and sample size the obtained distribution of t departs significantly from the theoretical distribution. As reported in other studies, e.g., Welch (1937) and Boneau (1960), when the sample with the smaller variance also has the smaller samples size, the proportion of obtained t's is much less than expected, and when the sample with the smaller variance has the larger n, the proportion of t's obtained is much more than expected.

2. When sampling from the same nonnormal distributions such as both positive skewed or leptokurtic distributions, the obtained distributions of t match the theoretical distributions when the samples are equal in size and variance. However, with equal n's but different variances, the distributions of t are skewed and the resulting proportions are significantly different than expected for the skewed distributions, Contrary to the results of Boneau (1960), this discrepancy does not diminish with larger samples, e.g., n = 30 for both samples. With combinations of differences in both n and variance, the results are similar to these combinations as noted above but are more extensive.

3. When sampling from two different nonnormal distributions, the obtained distributions of t depart significantly from the theoretical distributions even when the samples are of the same size and have the same variance. When the sampling is from distributions

34 NEGATIVESKEW STANDARD DEVIATION =16 N=109000 INT PER ORD FREQ

0 0.095 -3.09860 19.000 1 0.310 -1.79817 24.000 2 0.565 -0.75783 27.000 3 0.790 -0.15096 18.000 4 0.980 0.45590 20.000 5 1.200 1.58294 24.000 6 1.435 3.40354 23.000 7 1.645 3.75032 19.000 8 1.875 5.39753 27.000 9 2.135 6.52456 25.000 10 2.400 8,34516 28.000 11 2.670 8.95203 26.000 12 2.995 9.81898 39.000 13 3.385 11.72627 39.000 14 3.785 12.85331 41.000 15 4.15 0 13.98035 32.000 16 4.515 15.71425 41.000 17 4.945 17.01468 45.000 18 5.380 17.44815 42.000 19 5.805 18.05502 43.000 70 6.265 19.00867 49.000 21 6.770 20.48248 52.000 22 7.315 20.91596 57.000 23 7.900 22.47647 60.000 24 8.465 24.64385 53.000 25 9.030 24.90394 60.000 26 9.600 25.42411 54.000 27 10.225 27.15801 71.000 28 10.955 27.50479 75.000 29 11.645 29.32539 63.000 30 12.310 30.36573 70.000 31 13.015 31.57946 71.000 32 13.760 32.09963 78.000 33 14.585 33.40006 87.000 34 15.525 34.70049 101.000 35 16.510 35.39405 96.000 36 17.630 36.60778 128.000 3.7 18.790 38.08160 104.000 38 19.875 38.86186 113.000 39 21.060 41.02924 124.000 40 22.315 41.46271 127.000 41 23.740 41.63610 1580000 42 25.190 42.24297 132.000 43 26.550 42.32966 140.000 44 28.165 42.507105 183.000 45 29.955 43.10992 175,000 46 31.640 43.97687 162.000 47 33.535 44.75713 217.000 48 35.690 46.83781 214.000 49 37.790 48.74510 206.000

A-8 which are skewed in opposite directions, the obtaineddistributions of t are also skewed. Significant discrepancies were found between obtained and theoretical proportions of t for all combinations of n's and variances. Even with n = 30 for both groups and with equal variances tl.e proportion of t's were significantlydifferent than expected. For combinations of differences in bothn's and variances, the same trend is noted as before.

4. When sampling from two different distributions one of which is normal and the other skewed, the obtaineddistribution of t also tends to be skewed even for equal n's andvariance. Again, contrary to the results of Boneau (1960), thedistributions of t remain skewed and there are significant discrepanciesfrom expected even with n's of 30. Thus the effect of increasing the sample size does not normalize the obtained distribution asreadily as Eoneau found. With various combinations of unequal n's and variances, the same results occur with these distributions asnoted with other distributions.

In this study, the t test was found to be quitesensitive to certain violations of its basic assumptions. Departures from normality seemed to produce significant discrepanciesbetween theoretical and obtained distributions of t even for samples with equal n's and variances. Thus the t -test does not seem to be "functionally nonparametric or distribution -free" as Boneau states (1960, p. 63). Significant discrepancies between the nominal and actual level of significance were found for manycombinations of violations of the basic assumpticns. Thus it is suggested that researchers carefully consider all of the assumptionsunderlying the t test before applying it in all situations. As pointed out in this study, failure to satisfy all of the assumptionsunderlying the t-test often alters the probability of a Type I error.Thus the experimenter may be in the position of having far greater orfar fewer chances of rejecting a true null hypothesis than herealizes, and the conclusions that he reaches might be due to the effects ofviolations of assumptions rather than treatment effects.

35 50 39.945 49.61206 225.000 51 42.240 50.47901 234.000 52 44.500 52.38630 218.000 53 46.645 54.46699 231.000 54 48.780 55.24724 216.000 55 51.060 56.11419 240.000 56 53.545 56.72106 257.000 57 56.255 56.89445 285.000 58 59.025 56.98114 269.000 59 61.730 57.58801 272.000 60 64.605 57.76140 303.000 61 67.790 58.19488 334.000 62 70.955 60.36226 299.000 63 74.025 61.14251 315.000 64 77.285 62.61633 337.000 65 80.520 63.83006 310.000 66 83.615 64.52362 309.000 67 86.510 65.82405 270.000 68 89.425 67.12448 313.000 69 92.290 67.64465 260.000 70 94.680 68.85838 218.000 71 96.810 69.89872 208.000 72 98.795 71.71932 189.000 73 99.870 72.06610 26.000 74 100.000 73.80000 0. 75 100.000 74.32018 0. 76 100.000 74.58026 0. 77 100.000 76.74764 0. 78 100.000 78.30815 0. 79 100.000 78.74163 0. 80 100.000 80.21545 0. 81 100.000 81.16909 0. 82 100.000 81.77596 0. 83 100.000 82.20944 0. 84 100.000 83.50986 O. 85 100.000 85.24377 0. 86 100.000 86.37080 0. 87 100.000 87.49784 0. 88 100.000 89.40513 0. 89 100.000 90.27209 0. 90 100.000 90.87895 O. 91 100.000 92.69955 0. 92 100.000 93.82659 0. 93 100.000 95.47379 O. 94 100.000 95.82058 0. 95 100.000 97.64117 O. 96 100.000 98.76821 0. 97 100.000 99.37508 0. 98 100.000 99.98194 0. 99 100.000101.02228 O. 100 100.000102.32271 0.

A-9 Table 1

SUMMARY TABLE OF ACTUAL PROBABILITIES OF TYPE I ERRORS WITH A ONE-TAILED t TEST FOR VARIOUS COMBINATIONS OF POPULATION SHAPES, POPULATION VARIANCES, AND n's

Nominal Level of Significance Sample A Sample B .05 .01 Shape n Left Right Left Right Shape or n 0-

Nor 4 5 Nor 4 5 .049 .049 .008 .010 No 4 5 Nor 8 5 .056 .060 .014 .012 Nor 4 5 Nor 4 15 .042 .051 .008 .010 Nor 4 5 Nor 8 15 .017* .015* .001 .002 Nor 4 15 Nor 8 5 .118* .115* .045* .041* Nor 4 5 + Skew 4 5 .030* .080* .004 .024 Nor 4 5 + Skew 8 5 .023* .110* .003 .039* Nor' 4 15 + Skew 8 15 .030* .084* .003* .030* Nor 4 30 + Skew 8 30 .0308 .074* .004 .021 Nor 4 5 + Skew 4 15 .032 .079* .003 .024 Nor 4 5 + Skew 8 15 .004* .046 .000 .012 .001 .012 Nor 4 15 + Skew 8 30 .011* .044 Nor 4 15 + Skew 8 5 .085* .157* .026 .064* Nor 4 30 + Skew 8 15 .071* .124* .015 .049* .011 Nor 4 f) Lep 4 5 .042 .046 .007 .C14 Nor 4 1.% Lep 8 5 .051 .050 .013 Nor 4 5 Lep 4 15 .043 .048 .010 .011 Nor 4 5 Lep 8 15 .014* .016* .001 .002 Nor 4 5 Lep 8 5 .126* .115 .045* .039* + Skew 4 5 + Skew 4 5 .041 .042 .007 .006 + Skew 4 5 + Skew 8 5 .029* .105* .006 .031* + Skew 4 30 + Skew 8 30 .033 .075* .003 .022 + Skew 4 5 + Skew 4 15 .033 .065 .001 .017 + Skew 4 5 + Skew 8 15 .002* .041 .000 .009 + Skew 4 15 + Skew 8 5 .093* .145* .031* .055* + Skew 4 30 + Skew 8 15 .069 .113* .016 .042* + Skew 4 5 - Skew 4 5 .110* .017* .046* .002 + Skew 4 5 - Skew8 5 .123* .021* .052* .002 + Skew 4 30 - Skew 8 30 .079* .031* .003 + Skew 4 5 Skew 4 15 xe2* .036 .028 .006 + Skew 4 5 - Skew 8 15 .043 .007* .012 .000 + Skew 4 15 - Skew8 15 .178* .086* .094* .025 + Skew 4 5 Lep 4 5 .073* .027* .021 .003 + Skew 4 5 Lep 16 5 .058 .051 .023 .020 + Skew 4 5 Lep 4 15 .049 .038 .010 .010 + Skew 4 5 Lep 16 15 .003* .005* .001 .001 + Skew 4 15 Lep 16 5 .183* .177* .095* .087* Lep 4 5 Lep 4 5 .044 .042 .007 .006 Lep 4 5 Lep 16 5 .055 .052 .018 .018 Lep 4 5 Lep 4 15 .044 .049 .009 .008 Lep 4 5 Lep 16 15 .005* .006* .001 .001 Lep 4 15 Lep 16 5 .171* .172* .080* .086*

*One-Tailed Tests

36 LEPTOKURTICDISTRIBUTION STANDARD DEVIATION =16N=1Ut000 TNT PER ORD FREQ

0 0.020 -10.70250 4.000 1 0.070 - 9.20930 6.000 2 0.150 - 8.01474 10.000 3 0.230 -7.31791 6.000 4 0.315 -6.62109 11.000 5 0.420 -5.32698 10.000 6 0.510 - 3.23650 8.000 7 0.605 -2.83832 11.000 8 0.735 - 0.94693 15.000 9 0.875 0.34717 13.000 10 0.960 2.43765 4.000 11 1.020 3.13448 8.000 12 1.155 4.12994 19.000 13 1.305 6.31997 11.000 14 1.410 7.61408 10.000 15 1.510 8.90818 10.000 16 1.655 10.89911 19.000 17 1.815 12.39231 13.000 18 1.940 12.89005 12.000 19 2.130 13.58687 26.000 20 2.375 14.68188 23.000 21 2.575 16.37418 17.000 22 2.765 16.87191 21.000 23 2.945 18.66375 15.000 24 3.145 21.15241 25.000 25 3.355 21.45105 17.000 26 3.600 22.04833 32.000 27 3.910 24.03926 30.000 28 4.165 24.43745 21.000 29 4.395 26.52793 25.000 30 4.660 27.72249 28.000 31 4.920 29.11614 24.000 32 5.230 29.71342 38.000 33 5.595 31.20662 35.000 34 5.970 32.69982 40.000 35 6.370 33.49619 40.000 36 11.060 34.88984 898.000 37 18.400 36.58213 570.000 38 23.200' 37.47805 390.000 39 26.575 39.96672 285.000 40 29.310 40.46445 262.000 41 31.835 40.66354 243.000 42 34.200 41.36037 230.000 43 36.400 41.45992 210.000 44 38.470 41.65901 204.000 45 40.430 42.35584 188.000 46 42.250 43.35130 176.000 47 44.075 44.24722 189.000 48 45.815 46.63634 159.000 49 47.390 48.82637 156.000

r A-10 '..' r

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37 50 49.070 49.82183 180.000 51 50.925 50.81730 191.000 52 52.815 53.00732 187.000 53 54.665 55.39644 183.000 54 56.485 56.29236 181.000 55 58.380 57.28783 198.000 56 60.300 57.98465 186.000 57 62.215 58.18375 201.000 58 64,490 58.28379 250.000 59 67.025 58.98012 257.000 60 69.720 59.1.7921 282000 61 72.700 59.67694 314.000 62 76.21.5 62.16561 389.000 63 81.020 63.06153 572.000 64 88.720 64.75382 968.000 65 93.765 66.14747 41.000 66 94.120 66.94385 30.000 67 94.420 68.43704 30.000 68 94.680 69.93024 22.000 69 95.010 70.52752 44.000 70 95.395 71.92118 33.000 71 95.665 73.1.1573 21.000 72 95.950 75.20621 36.000 73 96.270 75.60440 28.000 74 96.500 77.59533 18.000 75 96.695 78.19261 21.000 76 96.850 78.49125 10.000 77 96.990 80.97992 18.000 78 97.195 82.77175 23.000 79 97.410 83.26949 20.000 80 97.580 84.96178 14.000 81 97.710 86.05679 12.000 82 97.815 86.75362 9.000 83 97.940 87.25135 16.000 84 98.090 88.74455 14.000 85 98.255 90.73548 19.000 86 98.460 92.02959 22.000 87 98.645 93.32369 15.000 a88 98.750 95.51372 6.000 89 98.845 96.50918 13.000 90 98.980 97.20601 14.000 91 99.095 99.29649 9.000 92 99.210100.59059 14.000 93 99.355102.48198 15.000 94 99.47010288017 8.000 95 99.545104.97064 7.000 96 99.62510626475 9.000 97 99.725106.96158 11.000 98 99,830107.65840 10.000 99 99.925108.85296 9.000 100 99.985110.34616 3.000

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38 APPENDIX B

TABLES OF SAMPLING DISTRIBUTIONS OF THE

t RATIO OBTAINED PERCENTAGES OF t VALUES Normal = 5 ) and TABLE FOR GIVEN LEVELS OF SIGNIFICANCEB - Normal (N = 5 ) DISTRIBUTIONS FOR Int. - Int. A Scales B .0010 .0038.0050 .0084.0100 .0220.0250 Levels of Significance .0500.0492 .0499.0500 .0244.0250 .0098.0100 .0046.0050 .0012.0010 Int. - Per.Ord. .0098.0016 .0172.001 .0222.0090 .0230 .0486.0632 42532..0750* .0286.0502* .0304*.0112 ,0072 .0014.0102 Ord.Ord. - -Ord. Int. .0012 .0050.0048, ,1104.0104 .0258.02600426 .0500.0534 .9516.0474 .0274.0262 .0112.0100 SQLQ,Oali.0072 0020.0020 Per.Ord. - Int.Per. .0120.0096 .0240.0174 .0332*.0264 .0528*.0434 .0770*.0638 .0674.0744* .0440.0504* .0278.0306* .0216.0212 .0114.0100 kixA Per. - Ord.Per. .0018.0122 .0062.0238 .0108.0336* -0250.0518* .0504.0750* .0504.0690 .0294,.0436 .0114.0278 .0220.0070 .0114.0020 Interval SampleOrdinal A Percentile Descriptions of Samples Interval49.997 ,:_Sample B 49.924Ordinal Percentile 49.452 MeanSDMeans of ofMeansof SDsMeans 50.003 1.8073.360 49.941 1.8043.428 49.56424.72112.990 3.4011.798 1.7913.457 24.90712.870 MeanSD of of SDs Skews -0.011 1.199 -0.009 0.987 -0.005 6.907 -0.001 0.6091.207 -0.003 0.9790.593 0.5880.0066.852 MeanSD of SkewsKurtosis -0.998 0.6140.507 -1.075 0.6150.594 -1.106 0.5200.594 -0.993 0.494 -1.062 1.164 -1.109 0.515 OBTAINED PERCENTAGES OF t VALUES FOP GIVEN LEVELS OF SIGNIFICANCE Normal = 5 ) and TABLE B Normal 2 (N = 5 ) DISTRIBUTIONS FOR Int. - Int. A Scales B .0006.0010 .0052.0050 .0094.0100 .0250.0256 Levels of Significance .0472.0500 .0456.0500 .0240.0250 .0092.0100 .0042.0050 .0008.0010 Int. - Per.Ord. .0048.0010 .0122.0062 .0188.0100 .0342.0238 .0568.0458 .0610.0494 .0384.0256 .0208.0112 .0130.0054 .0008.0040.0012 Ord. - Ord.Int. .0018 .0072.0062 .0120.0118 .0260.0276 .0490.0494 .0474.0444 .0232.0258 .0100.0112 .0130.0060.0054 .0040.0010 us Ord. - Per. .0058.0048 .0150.0124 .0220.0188 .0352.0336 .0644.0572 .0574.0606 .0370.0368 .0200.0206 .0132 .0032 t.J 1 Per.Per - Ord. - Int. .0048 .0142 .0212 .0348 .0628 .0592 .0376 .0204 .0132 .0038 Per. - Per. .0022 .0062 Sample A .0116 .0260 Descriptions of Samples .0482 .0488 .0250 Sample B .0108 .0066 .0012 C:7 SDMeans of Meansof Means Interval50.015 1.793 49.947Ordinal 1.788 Percentile 49.869 4.288 Interval 50.020 1.807 Ordinal49.952 1.788 Percentile 49.883 4.284 MeanSD of SDsSkewsSDs -0.003 1.2123.361 -0.010 0.9903.428 -0.002 8.2442.319 -0.003 1.2643.413 -0.005 1.0083.462 -0.004 2.3468.310 MeanSD of KurtosisSkewsKurtosis -1.004 0.5050.614 -1.075 0.7100.597 -1.113 0.5220.592 -1.000 0.6120.499 -1.083 0.5390.597 -1.113 0.5200.591 TABLE B - 3 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN Normal (N = 5 ) and Normal LEVELS OF SIGNIFICANCE FOR (N = 5 ) DISTRIBUTIONS Int. - Int. A Scales B .0034.0010 .0104.0050 ,0158.0100 .0250 Levels of Significance .0500.0610 ,0614.0500 .0328.0250 .0174.0100 _Cala.0050 .0010 nn19 Int. - Per.Ord. .0078.0032 .0098.0174 .0250.0156 _dux.0424.0310 .0654.0570 .0726*.0630 .0450*.0356. 3.0192.0282 _0112.0204 _ackaa Ord. - Int.Ord. .0034 .0102.0100 .0158.0160 .0318.0350 .0588.0628 .0636.0602 .0352.0320 .0188.0170 .0108.0090 ,0032.0030 02 Per.Ord. - Int.Per. .0030.0082 .0112.0178 .0168.0262 .0332.0428 .0616.0662 .0546.0724* .0332.0442* .0176.0276 .0106.0202 ,20.4..0082 1.4 1 Per. - Ord. .0026 .0110 .0170 .0328 .0606 .0504.0574 .0304.0352 .0148.0194 .0076.0110 .0016.0048 Per. - Per. .0020 Interval .0064 OrdinalSample A .0110 Percentile.0252 Descriptions of Samples .0520 Interval OrdinalSample B Percentile SDMeans of Meansof Means 50.007 1.822 49.940 1.809 12.99449.572 13.90050.056 7.321 13.51749.772 7.160 12.78249.63924.936 MeallSDMean of ofofSDs SDsSkews 0.0031.2313.386 0.9900.0053.440 24.773 0.0076.918 -0.001 5.123 0.0025.130 -0.000 7.011 MeanSDSD of of Skews KurtosisKurtosis -0.994 0.5130.615 -1.079 0.5490.595 -1.101 0.5990.526 -1.002 0.6170.501 -0.988 0.5110.630 -1.117 0.5200.592 TABLE B - 4 OBTAINED PERCENTAGES OF t VALUES FOR Normal (N - 5 ) and GIVENNormal LEVELS. OF SIGNIFICANCE FOR (N = 5) DISTRIBUTIONS A Scales B .0010 .0050 .0100 .0250 Levels of Significance .0500.0560 .0500.0602 .0250.0332 .0100.0124 .0050.0058 .0010.0016 Int. - Int.Ord. .0034.0044.0020 .0122.0098.0060 .0196.0158.0140 .0386.0350.0318 .0584.0576 .0690.0634 .0428.0374 .0212.0190 .0144.0112 .0052.0040 Ord.Int. - -Int. Per. .0020 .0100.0070 .0158.0148 .0352.0324 .0574 .0634.0588 .0314.0342 .0192.0122 .0106.0060 .0032.0022 Ord. - Per.Ord. .0032.0042.0040 .0096.0122 .0158.0198 .0346.0376 .0588.0582 .0538.0672 .0256.0434 .0122.0220 .0068.0150 .0014.0044 to 1 Per. - Int. .0268 .0120 .0068 .0020 s... Per. - Per.Ord. .0024.0030 .0094 .0134.0148 .0304 .0550.0560 .0560.0564 .0276 .0116 .0066 .0018 Interval OrdinalSample A Percentile Descriptions of Samples Interval OrdinalSample B Percentile 49.903 MeanSDMeans of of Meansof SDs Means 50.011 3.3871.827 49.950 3.4391.810 49.873 4.3328.253 50.040 6.6563.541 49.937 6.6853.538 8.2294.289 MeanSD of SDsSkews 0.0071.224 0.0050.993 0.0112.310 0.0062.387 0.0042.226 0.5920.0142.306 SDMean of ofKurtosisSkews Kurtosis -1.002 0.6140.506 -1.067 0.5941.079 -1.114 0.5220.590 -0.999 0.5050.618 -1.061 0.6430.581 -1.111 0.522 TABLE B 5 OBTAINED PERCENTAGES OF t Normal (N =15 ) and VALUES FOR GIVEN LEVELS OF Normal (N =15 ) DISTRIBUTIONS SIGNIFICANCE FOR A Scales B .0010 .0050 .0100 .0250 Levels of Significance .0500 .0500 .0250 .0100 .0050 T. -.0010 - Int. - Int. .0014.0012 .0040 .0100.0098 .0244.0220 .0478..1142A .0440.0486 .0204.0232 Askaa.0072 Alin.0030 _nma.00Q4 Int. - Per.Ord. .0032 .0072 .0114 .0280 .051a .0578 2.2122..0306 .0064.0142 _Qua,0030 .0004.0028 Ord. - Int. Ord. .0016.0012 .0044.0048 .0102.0094 .0248.0270 .0458.0504 .0438.0472 .0212 .0986 ,0030.0078 .0028.0000 to Ord. - Per. .0036.0032 .0086.0074 .0168.0120 .0290.0342 .0600.0518 .0464.0572, .0248.0316 .0116.0140 .0062 .0016 Per.Per. - -Ord. Per. Int. .0038.0016 .0084.0050 .0088.0164 .0240.0340 .0474.0586 .0458.0476 .0202.0244 .0082.0116 .0034.0066 .0004.0020 `j Interval OrdinalSample A Percentile Descriptions of Samples Interval50.008 49.947OrdinalSample B Percentile 49.614 MeanSDMeans of of Meansof SDs Means 50.002 3.8031.027 49.937 1.0243.830 49.53427.579 7.374 1.0313.798 1.0283.826 27.5337.402 MeanSD of SDsSkews _0.002 0.710 -0.001 0.3730.514 0.3840.0073.514 -0.009 0.7160.521 -0.006 0.5160.371 -0.000 0.3823.518 MeanSDSD.of of of Skews Kurtosis -0.383 0.5260.785 -0.969 0.480 -1.047 0.432 -0.375 0.782 -0.965 0.478 -1.043 0.429 B - 6 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS Normal (N =30 ) and TABLE Normal' (N =30 ) DISTRIBUTIONS OF SIGNIFICANCE FOR Int. - Int. A Scales B .0004.0010 .0050 .0100 .0244.0250 Levels of Significance .0462.0500 .0500 .0226.0250 .0098.0100 .0048.0050 .0012.0010 Int. - Per.Ord. maL.0004 A042.0048.0040 ,000AgfaJIM .0214.0196 .0420.0414 ,0514AAA.0514 ,0254.0244 .0110.0108 .0062.0064 .0014.0014 Ord. - Int.Ord. .0006 ,0048,0056 AIM.0092 A22,1,0256 .0478.0528 .0460.0380 .0226.0208, .0092.0078 .0040.0036 .0012.0014.0010 to Per.Ord. - Int.Per. AMC.0006 .0058.0050 .0112.0104 .026k.0240, .0512.0456 .0398.0458 .0206.0226 .0078.0100 .0036.0052 .0014 a' i Per. - Per.Ord. .0004.0002 .0044.0046 :0090.0094 .0234.0228 .0470.0466 .0466.0464 .0230.0220 .0092.0096 .0050.0042 011 Interval OrdinalSample A Percentile Descriptions of Samples Interval OrdinalSample B Percentile 49.933 Alla MeanSDMeans of ofMeansof SDs Means 50.006 0.7323.912 49.942 0.7303.917 49.928 4.6970.876 50.007 0.739 49.944 0.7353.925 4.7030.878 MeanSD of SDsSkews 0.0030.517 -0.001 0.359 0.0080.408 -0.005 0.4120.5123.926 -0.003 0.2670.356 0.2690.0080.402 SDMean of ofSkewsKurtosis Kurtosis -0.189 0.7120.410 -1.019 0.3400.263 -1.114 0.2610.265 -0.174 0.724 -1.014 0.347 -1.111 0.261 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN TABLE B - 7 LEVELS OF SIGNIFICANCE FOR Scales B .0010 .0050 Normal .0100 (N =15 ) and .0250 Levels of Significance .0500 Normal .0500 (N =15 ) DISTRIBUTIONS .0250 .0100 .0050 .0010 Int.Int. - -Int. Ord. A .0018.0022 .0074.0084 .0134.0148 .0294.0332 .0522.0586 2,1173..0640 .0346.0302 01E8.0148 .0094.0084 .0014.0020 Ord.Int. - -Int. Per. .0032.0026 .0086.0094 .0162.0150 .0348.0304 .0594.0568 .0572.0652 A298.(118, .0140.0186 .0078.0124 .0012.0Q32 Ord.Ord. - -Ord. Per. .0020.0036 .0098.0072 .0154.0144 .0308.0312 .0576.0534 .0638.0616 .0376.0344 .0180.0158 .0120.0094 .0030.0016 w Per. - Ord.Int. .0016 .0054.0066 .0118.0124 .0280.0306 .0568.0592 .0462.0434 .0270.0248 .0112.0096 .0056.0060 .0016.0014.0020 Per. - Per. .0008 .0068 Sample A .0114 .0288 Descriptions of Samples .0552 .0486 .0262 SampleOrdinal B .0110 Percentile .0066 SDMeans of Meansof Means Interval49.989 1.023 49.921Ordinal1.025 Percentile 49.44Q 7.377 Interval49.99(1 4.269 49.719 4.182 49.556 7.538 MeanSD of ofSDs SkewsSDs 0.0050.7253.817 0.0020.5203.835 27.605 0.0133.532 -0.01015.514 3.029 -0.01015.163 3.057 27.5650.0053.659 MeanSD of KurtosisSkews -0.363 0.7780.526 -0.961 0.4750.375 -0.041 0.4210.384 -0.368 0.7700.517 -0.266 0.8240.554 -1.038 0.4470.385 OBTAINED PERCENTAGES OF t VALUES FOR TABLE B-8GIVEN LEVELS OF SIGNIFICANCE FOR A Scales B .0010 .0050Normal .0100 (N = 5 ) and .0250 Levels of Significance .0500 Normal .0500 (N 1115 ) DISTRIBUTIONS .0250 .0100 .0050 .0010 Int. - Int. .0004 .0040 .0064.0078 .0162llit 0411 ,025 .0254.0252 ,0120,0116 .0054.0050 .0010.0010, Ord.Int.Int. - -Int.Ord. Per. ,0900,0004 ,ffla.0002.0046 .0080.00Q2 .0230.0016* 0112.0466.0034* .0524.0066* .0254.0026* .0016.0108 .0052.0004 .0012.0000 Ord. - Per.Ord. ,0210.0000.0006 .0042.0002 .0080.0002 .0200.0014* .0036*.0410 .0066*.0506 .0026*.0262 .0118.0016 .0004.0060 .0000.0012 coai Per. - Ord.Int. .0530*.0534* .0830*.0834* .1060* .1386*.1418* .1830*.1818* .1780*.1788* .1416*.1410* .1058*.1050* .0866*.0862* .0558*.0564* Per. - Per. .0006 .0044 Sample A .0076 .0202 Descriptions of Samples .0408 .0542 .0266 Sample B .0120 .0056 .0012 SDMeans of Meansof Means Interval50.023 1.761 49.963Ordinal 1.761 Percentile 12.65649.724 Interval49.992 1.021 49.927Ordinal 1.021 Percentile 49.455 7.344 MeanSD of ofSDs SkewsSDs 0.0151.2273.366 0.0070.9993.440 24.807 0.0136.973 0.0020.7213.789 0.0030.5183.819 27.493 0.0133.549 MeanSDSD of of Skews Kurtosis -1.006 0.5030.607 -1.078 0.5710.597 -1.113 0.5250.590 -0.370 0.7730.519 -0.960 0.4690.371 -1.036 0.4290.384 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN TABLE B - 9 LEVELS OF SIGNIFICANCE FOR Scales Normal (N = 5 ) and Levels of Significance .0500 Normal .0500 (N =15) DISTRIBUTIONS .0250 .0100 .0050 .0010 Int. - Int. A B .0010.0008 .0050.0038 .0100.0118 .0250.0270 .0532.0486 .0504.0506 .0232.0234 .0090.0082 .0048.0052 .0002.0006 Int. - Ord.Per. .0000.0006 .0002.0034 .0092.0006 .0236.0030* .0102* .0.472.0128* .0056*.0246 .0016.0094 .0050.0006 .0008.0002 Ord. - Int.Ord. .0010.0008 .0042.0056 .0130.0108 .0300.0256 .0530.0580 .0122*.0484 .0232.0050* .0088.0014 .0004.0034 .0002.0006 Per.Ord. - Int.Per. .0000.0232* .0492*.0004 .0714*.0008 .0020*,1076* .1474*.0108* .1276*.1250* .0864*.0882* .0572*.0564* .0408*.0400* .0196.0200 Per.Per. - -Ord. Per. .0006.0236* .0036.0488* .0692*.0108 .0256.1044* Descriptions of Samples .0534.1454* .0494 .0242 .0088 .0040 .0006 Interval 49.916OrdinalSample A Percentile 49.799 Interval 49.997 OrdinalSample49.930 B Percentile 49.829 MeanSDMeans of of Meansof SDs Means 49.972 1.7863.402 1.7693.457 8.3024.232 3.8081.046 3.8311.0370.523 2.4931.1879.190 MeanSD of ofSDs Skews -0.015 1.223 -0.008 0.9920.586 -0.002 2.3020.579 0.0070.7350.520 0.3710.005 0.3810.011 MeanSDSD of of Skews Kurtosis -1.003 0.6040.499 -1.077 0.733 -1.116 0.516 -0.396 0.780 -0.975 0.475 -1.053 0.425 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN TABLE B - 10 LEVELS OF SIGNIFICANCE FOR A Scales B .0010 .0050Normal .0100 s. 5) and Normal .0250 Levels of Significance .0500 .0500 (N MI5) DISTRIBUTIONS .0250 .0100 .0050 .0010 Int. - Ord.Int. .0010.0014 .0044.0052 .0092.0100 .0230.0258 .0650 0509 AlmAlai .0270.0266 .0128.0128 Alla 0056 .0008.0010 Ord.Int. - -/nt. Per. .0014.0096 .006200,4 .0114.0054 .0308.0146 _nk& ..11i2h. 0194 .0274.0200 .0072.0128 Jana.0060 .0002.0010 Ord. - Per.Ord. .0006.0012 .0030 0062 .0060.0114 .0276.0156 DOI.0568.0382 ...WI/ .0370 .0714_0280 .0076.0124 .0064.003Q .0002 pa t Per. - /nt. .0036 .0116 ,0216 .0456* .0808* .0696* .0386 .0184 Allfi .0032 o1-. Per. - Per.Ord. :0012.0032 .0056.0100 .0104.0194 .0270.0408 mkt.0562, .0518.0696 *. .0280.0388 .0198.0126 .0116.0060 .0026.0008 Interval OrdinalSample A Percentile Descriptions of Samples Interval 49.926OrdinalSample B Percentile 49.912 LfJ MeanSDMeans of of Meansof SDs Means 49.999 3.4151.829 49.925 1.8213.459 49.909 4.1452.183 49.992 3.8221.041 3.8371.041 4.6041.247 MeanSD of of SDs Skews 1.2320.005 0.9940.006 0.0081.154 -0.001 0.724 0.0040.5240.375 0.3850.0110.597 MeanSD of KurtosisSkews -0.991 0.5050.621 -1.068 0.8690.594 -1.105 0.5950.524 -0.370 0.7960.519 -0.964 0.485 -1.041 0.436 B - 11 OBTAINED PERCENTAGES OF t Normal (N =15 ) and VALUES FOR GIVEN LEVELS TABLE. Normal (N =30) OF SIGNIFICANCE DISTRIBUTIONS FOR Int. - Int. A Scales B .0010 .0062.0050 .0108.0100 .0280.0250 Levels of Significance .0546.0500 .0538.0500 .0252.0250 ,0104.0100 .0044.0050 .0010 Int. - Ord.Per. ,21200Ma.0006 0048.0038 ,9278..0096 .0248 .0374.0488 .0486.0602 .0242.0292 .0114 .0030.0052 .0004.0012 Ord. - Int.Ord. .0010.0008 .0064.0080 .0132.0140 .02962=.0342 .0548.0580 .0524.0510 .0222.0266 ma.0088.0096 .0038.0046 .0012 Per.Ord. - Int.Per. .0018.0000 .Outs.0038 Aaaa n'n6 .0214 .0670.0432 .0594.0448 .0106.0204 Ala.0062 .0060.0032 .0004.0016 w 1 _am .0068 .0020 1-1- Per. - Ord.Per. al"- -wagAlfa. -01115.-sum ma0370 -0526.0656 .0630 ,0338.0268 jotsp.0102 .0046 .0006 mu Interval 49.936SampleOrdinal A Percentile 49.923 Descriptions of Samples Ala Interval 49.994 Ordinal49.931Sample B Percentile 49.915 MeanMeansSD of of MeansSDs Means 50.009 1.0313.792 1.0293.819 4.5841.233 0.7343.906 0.7353.914 4.6930.8840.412 MeanSD of ofSDs Skews 0.0120.717 0.0060.5150.364 0.5880.3770.016 -0.004 0.4100.528 -0.0010.3620.268 0.2720.012 SDSDMean of of Skews ofKurtosis Kurtosis -0.380 0.5110.766 0.9670.462 -1.042 0.419 -0.199 0.687 -1.015 0.334 -1.107 0.262 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN TABLE B - 12 LEVELS OF SIGNIFICANCE FOR A Scales B .0010 .0050 Normal .0100 5 ) and .0250 Levels of Significance .0500 Normal .0500 (N g,15 ) DISTRIBUTIONS.0250 .0100 .0050 .0010 Int. - Ord.Int. -sum Aiwa.0000 .0006 .0022*022* .0076*.0062* alb*.0072* .0p20*.0020* .00Q8.0006 Aoz.0004.0002 .0000 Ord.Int. - Int.Per. ...0000 -Qom_Mm Aga ,0024*.00zp* Aim*.0074* .0088*.0068*.0052* Aug*.0022*.001e Aplz.0010.0006 Agog.0002 .0000 Ord.Ord. - -Ord. Per. ,glaQa.0000 .0000 .0002.0006 .0018*.0022* .0046*.0064* .1018*.0078* .0700*.0040* .0422*.0016 .0294*.0002 .0000.0114 Per. - Ord.Int. ,1112.1.0120 .0284*.0286* .0442*.0448* ..0706*.0708* ..1108*.1122* .0476.1064* .0248.0724* .0086.0456k .0038.0324 .0010.0130 Per. - Per. .0022 Interval .0044 OrdinalSample A .Q984 Percentile.0230 Descriptions of Samples .0494 Interval OrdinalSample B Percentile , SDMeans of Meansof Means 49.997 1.790 49.933 1.783 12.82249.502 50.069 4.265 49.800 4.157 27.59549.660 7.546 MeanSD of of SDs SkewsSDs -0.004 1.2503.402 -0.006 1.0063.455 24.866 6.972 15.497 0.0092.967 15.1340.0093.018 0.0113.596 MeanSDSD of of Skews Kurtosis -0.996 0.5010.613 -1.064 0,7010.394 -1.107 0.519'.7551 -0.376 0.7890.522 -0.282 0.8210.550 -1.039 0.3920.452 B - 13 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS Normal (N = 5) and 1ABLE Normal (N =15 ) DISTRIBUTIONS OF SIGNIFICANCE FOR Int. - Int. A Scales B .0010.000E, .0050.0004 .0012.0100 .C25u.00A4* Lgels of Significance .0500.0166* ,0146*.0500 .0250.0058 .0100.0018 .0050.0006 .0010.0002 Int. - Ord. - Per. .0000 .0002.0010 .0010 .0028*.0044* .0098*.0142* ,0140*.0122* .0042*.0056* .0010.0018 .0004.0006 .0002.0000 Ord.Ord.Int. - -Ord. Int. .0000 .0006.0004 .0014.008 .0050*.0054* .0164* 4178* .0146*.0140* .0062.0058 .0016 .0008 .0002 ra Per.Ord. - Int.Per. .0036.0000: .0130.0002 .0012.0218 .0468*.0028* .0760*.U06* .0694*.0120* .0384.0044* .0190.0014 .0120.0004 .0034.0000 Per. - Per.Ord. .0012.0032 .0046.0120 .0108.0212 .0270.0446* .0710*.0548 .0714*.0510 .0266.0390 .0108.0192 .0058.0126 .0014.0030 Interval OrdinalSample A Percentile Descriptions of Samples Interval OrdinalSample B Percentile 49.862 MeanMeansSD of of MeansSDs Means 50.005 3.3341.782 49.931 3.4081.784 49.840 8.1894.288 49.992 2.0847.591 49.897 2.0687.580 9.2142.499 MeanSD of SDsSkews 0.0201.203 0.0170.990 0.u232.320 -0.005 1.438 -0.005 1.321 0.3830.0181.168 MeanSDSD of of Skews Kurtosis -0.990 0.5070.623 2.6910.602 .958 -1.110 0.7330.596 -0.377 0.7980.524 -0.684 0.7670.516 -1.047 0.431 B - 14 OBTAINED PERCENTAGES OF t VALUES Normal (N = 5 ) and TABLE FOR GIVEN NormalLEVELS (N =15 ) DISTRIBUTIONS OF SIGNIFICANCE FOR Int. - Int. A Scales B .0002.0010 .0008.0050 .0020.0100 .0092.0250 Levels of Significance .0200*.0500 .0172*.0500 .0058.0250 _jaw_.0100 .0006.0050 .0000.0010 Int. - Ord.Per. .0004.0002, .0034.0006 .0018 .0076.0196 .0410.0200* .0180*.0462 .0068.0206 _oniz no14 .0030.0006 .0006.0000 Ord.Ord. - -Ord. Int. .0002 ,0008.0006 .0018gat.0024 .0084.0088 .0210*.0222* .0172.0164* * .0068.0060 .0016.0008 .0006.0004 .0002.0000.0006 ms Per.Ord. - Int.Per. .0002.0008 .0018.0048 .0046.0104 .0124.0216 .0292*.0444 .0234*.0440 .0094.0214 .0070.0028 .0008.0028 .0000 ss1-. 1 Per.Per. - -Per. Ord. .0020.0002 .0098.0012 .0152.0036 .0312.0116 .0300*.0616 .0576.0250* .0318.0096 .0122.0028 .0066.0010 .0002.0010 Interval OrdinalSample A Percentile Descriptions of Samples Interval50.015 49.913OrdinalSample B Percentile 49.941 MeanSDMeans of ofMeansof SDs Means 49.984 1.8203.404 49.923 1.8113.455 49.908 4.1482.170 2.0667.573 2.0587.367 1.2434.603 MeanSD of ofSDs Skews -0.001 1.236 0.0041.000 0.0071.161 -0.005 1.4550.517 -0.003 0.5111.324 0.5980.3860.017 SDMean of ofKurtosisSkews Kurtosis -0.997 0.6110.499 -1.080 0.5980.833 -1.103 0.5180.597 -0.383 0.766 -0.693 0.738 -1.042 0.432 B - 15 OBTAINED PERCENTAGES OF t VALUES FOR Normal (N =15 ) and Normal TABLE GIVEN LEVELS OF SIGNIFICANCE FOR (N = 30 ) DISTRIBUTIONS A Scales B -... .0010 .0050 .0100 .0250 Levels of Significance .0500 .0500 .0250 .0100 .0050 .0010 Int. - Ord.Int. .0002 jialaADJIL .0014_nni6 .0058,.0068 .0172*.0212* .0234,.0208* .0082.0064 .0014.0024 4.2011 .0008 ,19.20-Lima Ord.Int. - -Int. Per. .0002.0004 .11.00.1.0022 ,0038.0018 ,0078.0146, .0338.0214* .0182*.0404 .0046*.0292 .0052.0014 ,011.0004 .0004.0000 Ord.Ord. - -Ord. Per. .0008.0002 .0026.0008 ,0056.0012 .0074.0172 .(1177.0180* .0200*.0370 .0176.0070 .0048.0024 .0020.0008 .0000.0002 = 1 Per. - Int. .0002 .0016 .noin .0108 .0264* .0216* .0066 .0020 .0008 .0000 1-. Per. - Ord. .0002 .0012 .0026 .0084 .0230* .0246* .0096 .0030 .0010 Ago.0002 Per. - Per. .0014 Interval .0032 OrdinalSample A.0096 Percentile.0240 Descriptions of Samples .04913 .0454 Interval .0232 OrdinalSample B .0088 Percentile .0030 MeansSD of of Means Means 49.992 1.046 49.933 1.041 49.917 1.247 49.988 1.431 49.885 1.431 49.929 4.7130.862 MeanSD of SDsSkewsSDs -0.004 0.7333.817 -0.001 0.5243.834 0.5984.5940.008 -0.0077.8271.047 -0.008 0.9597.804 0.4120.021 MeanSDSD of of Skews Kurtosis -0.363 0.5290.803 -0.961 0.4960.375 -1.040 0.4420.385 -0.169 0.7260.410 -0.488 0.7360.418 -1.107 0.2660.263 TABLE B - 16 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE Normal (N =15 ) and Normal (N = 5 ) DISTRIBUTIONS FOR Int. - Int. A Scales B .0358*.0010 .0730*.0050 .0946*.0100 ,1282*.0250 Levels of Significance ,2728,.0500 .1766*.0500 .1296*.0250 . .0908*.0100 .0050 .0010 Int. - Per.Ord. .0344*0578* .0866*.0654* .1072*.0878* ..1262* .1780*.1676* .1960*ga* .1532*.1380* .0960* AMP.0722* .0374*.0368* Ord.Ord. - -Ord. Int. .0344*.0168* .0740*.0664* ..9822*.0962* ,IjAkt-UAW.1276* .1704*.1810* A2888*.1764* .1342*.1274* .0960*.0896* .0672* A618*.0386*.0358* to Per.Ord. - -Int. Per. .0004.05* ,QQaABU* .1084* Lin* .0260*.1798* .0170*.1940* alok.1518* 1128* .0008.0902* .0000.0620* cr, Per. - Ord.Per. 0004 ,0006 .0030,ma ,suat.0104 .0244* .0168* .0068 ALM.0020 .0008 .0000 .0004 Interval .0072 OrdinalSample A .0152 Percentile.0286 Descriptions of Samples .0572 .0550 Interval .0280 OrdinalSample B .0122 Percentile .0062 .0010 MeanSDMeans of of Meansof SDs Means 50.002 1.0453.802 49.9333.8231.046 27.52249.527 7.524 13.63650.003 7.341 13.26549.721 7.173 24.69112.94749.536 SDMeanSD of of Skews SDsSkews 0.0050.719 0.0010.517 0.0103.548 0.0084.904 0.0064.929 0.0146.908 SDMean of ofKurtosis Kurtosis -0.353 0.8030.537 -0.952 0.5000.383 -1.027 0.4650.397 -1.004 0.5030.615 -0.988 0.5150.630 -1.114 0.5210.593 TABLE B - 17 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE Normal (N = 15) and Normal (N = 5 ) DISTRIBUTIONS FOR Int. - Int. A Scales B .0106.0010 .0314*.0050 .0446*.0100 .0754*.0250 Levels of Significance .0500.1184* .1148*.0500 .0250.0738* .0100.0408* .0050.0272* .0010.0108 Int. - Ord. .0124 .0306* .0442* .0716*.0902* .1294*.1126* .1438*.1200* .0964*.0776* .0660*.0468* .0470*.0292* .0232*.0130 Ord.Int. - Int.Per. .0096.0232* .0318*.0450* .0446*.0578* .0746* .1192* .1098* .0712*.0762* .0460*.0390* .0282*.0258* .0130.0104 Ord. - Per.Ord. .0240*.0120.0000 .0028.0450*.0316* .0054.0590*.0442* .0134.0894*.0720* .0328.1324*.1126* .0306*.1398*.1164* .0134.0954* .0044.0634* .0022.0456* .0004.0236* 1-.w 1 Per. - Int.Ord. .0000 .0022 .0050 .0128 .0312 .0316 .0150 .0048 .0022 .0004 ...I Per. - Per. .0002 .0050 Sample A .0098 .0220 Descriptions of Samples .0460 .0412 .0242 Sample B .0088 .0046 .0008 SDMeans of Meansof Means Interval 50.003 1.037 Ordinal49.937 1.035 Percentile 49.845 2.480 Interval 49.992 3.566 Ordinal49.890 3.539 Percentile 49.852 4.289 MeanSD of SDsSkewsSDs 0.0050.7183.782 0.0030.5163.816 0.0129.1521.177 0.0042.4026.652 0.0016.6962.221 0.0162.3048.229 MeanSD of SkewsKurtosis 4 Kurtosis 0.7640.3780.520 0.4630.9670.369 -1.044 0.3810.418 -1.010 0.4980.607 -1.429 0.634 .554 -1.117 0.5150.587 TABLE B - 18 OBTAINED PERCENTAGES OF t VALUES FOR Normal (N s'15 ) and. Normal GIVEN LEVELS (N = 5 ) OF SIGNIFICANCE DISTRIBUTIONS FOR Int. - Int. A Scales B .0142.0010 .0314*.0050 .0484*.0100 .0808*.0250 Levels of Significance .123e.0500 .0500 .0250 .0490*.0100 .0330*.0050 ,0118.0010 Int. - Per.Ord. .0042.0154 .0312.0334* Allge .0410.0800* .0682.1198* .1296*Al& ABM'.0486*.0870* .0536* .0132,.0376* .0046.0168 Ord. - Int.Ord. .0138.0144 .0316*.0300* JaLO.0478*.0480* .0816*.0820* ..126e.1214* jase.1176*.1272* .0840*.0812* Ant.0522*.0478* .0312*.0362* .0118.0154 to Per.Ord. - Int.Per. .0102.0046 .0132.0228 .0354*.0208 .0654*.0412 .0694*.1078* .1014*.0762* .0630*.0432 .0196.0334* .0192.0116 .0068.0030 co1-. 1 Per. - Ord. .0100 .0234 .0344* .0664* .1036* .1068* .0684* .0388 .0240 .0088 Per. - Per. .0024 Interval .0086 OrdinalSample A .0148 Percentile.0308 Descriptions of Samples .0548 .0576 Interval .0282 OrdinalSample B .0114 Percentile .0060 .0010 MeansSD of of Means Means 49.994 1.041 49.934 1.043 49.921 1.250 49.984 3.567 49.885 6.6983.547 49.925 4.1152.152 MeanSD of ofSDs SkewsSDs -0.009 0.7313.799 -0.005 0.5283.824 4.5870.0030.597 6.6540.0072.420 0.0032.236 0.0161.166 MeanSD of KurtosisSkews -0.369 0.7850.523 -0.959 0.4850.380 -1.037 0.4360.390 -0.997 0.6150.499 -1.062 0.5960.639 -1.102 0.5330.597 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF TABU B - 19 SIGNIFICANCE FOR Scales B .0010 .0050 Normal .0100 (N =30 ) and .0250 Levels of SignificanceNormal .0500 .0500 (N = 15) DISTRIBUTIONS .0250 .0100 .0050 .0010 Int.Int. - Int.- Ord. A .0074' 0068 .0194.0718 ,012Fj,.0308* .0560*.0602* .0966*.0864* .1082* 1024* .0700*_0640* .0400*.0368* .0264*.0746* .nos.0074 Ord.Int. - Int.Per. .0024 .QUE-0228 015n .0614*.0330 .1018*.0584 .0774*.0970* ,04l0.0626* .0317*.0228 .0224.0128 _008..0076 Ord.Ord. - -Ord. Per. -osaa.0026.0076 .0214 0108 _0346*.0178.0310* .0584*.0358 .0636.0900* ,1022*.0712* Afia,.0396 .0374*.0194 .0248*.0112 .0028.0082 Per. - Int.Ord. .0060.0064 .0180.0182 .0264.0288 .0500*.0532* .0832*.0924* Ane.0876* .0568*.0542* .0314*.0290 .0204.0188 .0052.0052 Per. - Per. .0018 Interval .0076 OrdinalSample A .0144 Percentile.0292 Descriptions of Samples .0544 .0594 Interval .0324_ OrdinalSample B .0144 Percentile .0092 .0010 MeanMeansSD of of MeansSDs Means 50.003 0.7503.912 49.939 0.7433.915 49.925 0.8934.693 49.974 2.0987.610 49.870 2.0877.598 49.923 4.6111.254 MeanSD of SDsSkews 0.5200.003 -0.000 0.360 0.0100.409 -0.002 1.457 -0.004 0.5131.337 0.3810.0230.598 MeanSDSD of of Skews Kurtosis -0.173 0.7280.412 -1.010 0.3430.268 -1.107 0.2710.259 -0.381 0.5190.80/ -0.685 0.772 -1.044 0.444 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR TABLE B - 20 A Scales B .0010 .0050Normal .0100 (N = 5 ) andPositive Skewed(N = 5 ) DISTRIBUTIONS .0250 Levels of Significance .0500 .0500 .0250 .0100 .0050 .0010 Int. - Ord.Int. .00060004 z0030.0018 .0040.0062 .0158.0128 .0376.0300* .0690.0802* .0400.0476* .0200.0236 .0108.0142 .0024.0032 Ord.Int. - -Int. Per. .0080 ,0180.0024 .0258.0052 .0170.0440 .0342.0658 .0746*.0684 .0430,.0468* .0238..0294* .0226.0148 .0112 Ord. - Per.Ord. ,0006,.0078.0008 .0182.0034 .0266.0076 .0442*.0192 .0678.0394 .0690.0644 .0470*.0384 .0294*.0182 .0226.0114 A036.0112.0030 to Per. - Ord.Int. .0104 .0208.0206 .0294*.0296* .0490*.0488* .0712*.0718* .0674.0682 .0460*.0466* .0284.0284 .0204 .0098 Per. - Per. .0020 .0056 Sample A .0120 .0270 Descriptions of Samples .0534 .0526 .0294 Sample B .0126 .0066 .0018 MeansSD of of Means Means Interval50.013 1.795 49.944Ordinal 1.792 Percentile 12.89649.585 Interval49.959 2.590 49.996Ordinal 2.185 Percentile 49.968 4.861 MeanSD of SDsSkews 0.0121.2163.343 0.0130.9983.418 24.641 0.0156.979 0.4221.6293.167 0.3071.2833.328 24.883 0.0076.806 SDMean of ofKurtosisSkews Kurtosis -0.996 0.5060.617 -1.071 0.5730.602 -1.102 0.5250.597 -0.938 0.5940.597 -1.018 0.6510.605 -1.126 0.5260.594 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR TABLE B - 21 Scales B .0010 .0050 Normal .0100 (N =5 .0250 ) andPositive Skewed(N =5 Levels of Significance .0500 .0500 ) DISTRIBUTIONS.0250 .0100 .0050 .0010 Int. - Ord.Int. A .0006.0006 .0032.0022 .0056.0042 .0164.0120 .0392.0328 .0602.0708* .0424.0358 .0164.0204 .0098.0084 .0024.0026 Int. - Per. .0006.0042 .0120.0038 .0052.0210 .0164.0394 .0354.0648 .0668.0570 .0412.0352 .0186.0198 .0108.0140 .0030.0052 Ord. - Int.Ord. .0044.0006 .0122.0040 .0224.0072 .0410.0194 .0664.0438 .0572.0574 .0344.0332 .0194.0154 .0128.0088 .0044.0022 Per.Ord.Per. - -Int.Per. Ord. .0044.0048 .0128.0120 .0192.0204 .0396.0412 .0670.0648 .0594.0604 .0356.0376 .0182.0206 .0130.0132 .0048.0058 Per. - Per. .0026 .0062 Sample A .0118 .0290 Descriptions of Samples .0546 .0452 .0230 Sample B .0110 .0048 .0016 SDMeans of Meansof Means Interval50.030 1.825 49.963Ordinal1.808 Percentile 49.903 4.344 Interval50.040 1.797 50.072Ordinal 1.789 Percentile 50.1564.292 MeanSD of SDsSkews' - 0.003 1.2183.382 -0.008 0.9973.443 -0.003 2.3238.264 0.4331.6673.231 0.3081.3073.364 -0.004 2.3038.316 SDMean of ofKurtosisSkews Kurtosis - 0.995 0.5010.616 -1.070 0.6650.602 -1.106 0.5960.522 -0.914 0.5860.596 -1.003 1.1220.602 -1.110 0.5210.593 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF TABLE B - 22 SIGNIFICANCE FOR A Scales B .0010 .0050 Normal .0100 (N = 5 ) andPositive Skewed(N = 5 ) .0250 Levels of Significance .0500 .0500 .0250 DISTRIBUTIONS .0100 .0050 .0010 Int. - Ord.Int. .0002.0004 .0018 .0026 .0076.0084 .0182*.0210* .1668*.1482* .1134*.1022* .0770*.0662* .0600*.0482* .0222* Ord.Int. - Int.Per. .0004.0056 .0018.0126 .0026.0174 .0088.0316 .0214*.0446 .1472*.1012* .1018*.0670* .0656*.0420* .0474*.0290* .0218*.0136.0232* Ord. - Per.Ord. .0058.0002 .0130.0016 .0172.0026 .0314.0084 .0454.0180* .1004*.1616* .0674*.1122* .0414*.0766* .0290*.0572* .0140.0232* n)od Per.Per. - -Ord. Int. .0014 .0062.0058 .0128.0116 .0248.0248 .0452.0492 .0742*.0672 .0450*.0428 .0248.0222 .0174.0160 .0052.0046 Per. - Per. .0016 .0032 Sample A .0068 .0184 Descriptions of Samples .0368 .0716* .0406 Sample B .0184 .0102 .0032 SDMeans of Meansof Means Interval50.040 1.811 49.972Ordinal 1.796 Percentile 12.89849.785 Interval 49.934 8.E84 Ordinal48.326 7.295 Percentile 13.51146.294 f7 MeanSD of of SDs SkewsSDs 0.0021.2293.379 -0.000 0.9983.437 24.7450.0026.951 15.8000.4288.115 13.4760.3695.688 26.256 0.0437.216 'SD of KurtosisMeanSD of SkewsKurtosis -0.996 0.615 -1.068 0.597 -1.107 0.592 -0.936 0.592 -0.964 0.593 -1.132 0.588 -7' 0.510 0.655 0.519 0.576 0.562 0.526 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN Normal (N = 5 ) and Positive Skewed(N = 5 ) TABLE B 23 LEVELS OF SIGNIFICANCE DISTRIBUTIONS FOR A Scales B .0002.0010 .0050.0016 .0100.0032 .0076.0250 Levels of Significance .0500.0220 .1100*.0500 .0708*.0250 .0100.0390* .0050.0234 .0010.0078 Int.Int. - -Int. Ord. .0050.0004 .0116.0028 .0182.0038 .0384.0110 .0644.0248* .0608.1008* .0348.0680* .0186.0448* .0118.0292* .0056.0118 Ord.Int. - -Int. Per. .0002.0006 .0028.0012 .0044.0036 .0116.0094 .0268*.0236* .0992*.1142* .0648*.0670* .0374*.0366* .0214.0258* .0096.0070 Ord.Ord. - -Ord. Per. .0020.0046 .0062.0116 .0194.0090 .0388.0204 .0412.0652 .0668.0596 .0408'.0348 .0212.0178 .0120.0138 .0048.0052 Cf: 1.4no Per. - Ord.Int. .0016 .0060 .0102 .0206 .0442 .0652 .0378 .0190 .0120 .0048 Per. - Per. .0022 .0078 Sample A .0126 .0308 Descriptions of Samples .0528 .0464 .0230 Sample B .0116 .0064 .0022 MeansSD of of Means Means Interval49.978 1.795 49.920Ordinal 1.790 Percentile 49.797 4.292 Interval49.916 3.545 Ordinal50.038 3.534 Percentile 50.130 4.265 MeanSD of ofSDs SkewsSDs -0.005 1.2343.371 1.0033.4360.002 0.0062.3418.242 0.4243.2306.271 0.5193.1006.372 -0.013 2.2838.217 MeanSDSD of of Skews Kurtosis -1.006 0.5110.611 -1.086 0.6570.596 -1.117 0.5250.588 -0.927 0.6020.575 -.7561.579 .571 -1.110 0.5150.591 OBTAINED PERCENTAGES OF t VALUES TABLE FOR GIVEN LEVELS IS - 24 OF SIGNIFICANCE FOR A Scales B .0010 .0050Normal .0100 (N = 5 ) andPositive .0250 Levels of Significance .0500 Skewed(N .0500 = 5 ) DISTRIBUTIONS .0250 .0100 .0050 .0010 Int.Int. - -Ord. Int. .0008.0004 _noin_0072 .0066.0038 .0156.0114 .0326.026e -1012*.0936* .0634*.0652* .0366*.0356* .0272*.0232 .0074.0106 Ord.Int. - -Int. Per. .0004.0022 .0022.0094 .0044.0176 .0122.0352 .0298*.0618 .0942*.0456 .0626*.0254 .0326*.0124 .0206.0060 .0062.0010 Ord. - Per.Ord. .0022.0006 .4100.0u2 .0182.0062 .0362.0162 .0630.0342 .0890*.0440 .0238.0594* .0110.0346* .0058.0240 .0014.0084 w 1 Per. - Int. .0004 .0022 .0040 .0304* NI.p. Per. - Ord. .0008 .0030 .0060 .0166.0118 .0344 .0800*.0862* .0502*.0538* .0282.0278 .0172.0174 .0072.0058 . Per. - Per. .0026 .0098 Sample A .0168 0360 Descriptions of Samples .0634 .0434 .0250 Sample B .0206 .0058 .0010 SDMeans of Meansof Means Interval50.013 1.768 49.945Ordinal1.770 Percentile 49.932 2.124 Interval 50.129 3.610 Ordinal50.257 3.615 Percentile 50.163 2.143 MeanSD of SDsSkewsSDs -0.007 1.2073.360 -0.005 0.9873.430 -0.004 1.1514.120 0.4366.4513.374 0.4943.2126.529 -0.015 4.1281.172 SDMeanSD of of Kurtosis SkewsKurtosis -0.991 0.5040.612 -1.068 0.6400.594 -1.107 0.5870.525 -0.929 0.5790.594 -0.976 0.7810.615 -1.122 0.5270.586 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR TABLE B 25 A Scales B .0010 .0050Normal .0100 (N = 15) andPositive Skewed(N =15 ) DISTRIBUTIONS .0250 Levels of Significance .0500 .0500 .0250 .0100 .0050 .0010 Int.Int. - Ord.- Int. .0002.0000 :0010.0026 .0062.0042 .0186.0138 .0422.0332 .0516.0596 .0330.0290 .0124.0154 .0068.0094 .0024.0008 Ord.Int. - Int. - Per. .0002.0030 .0022.0094 .0050.0168 .0164.0334 .0396.0602 .0552.0508 .0304.0304 .0136.0134 .0084.0072 .0026.0024 ' Ord. - Ord. .0006 .0042 .0072 .0214 .0488 .0470 .0246 .0196 .0046 .0008 Ord. - Per. .0030 .0098 .0144.0174 .0340.0324 .0610 .0490 .0290 .0132.0124 .0072.0078 .0016.0018 = 1 Per. - Ord.Int. .0026 .0090.0088 .0140 .0326 .0620.0608 .0470.0486 .0258.0260 .0124 .0072 -0016 (4A wiNI Per. - Per. .0010 .0066 Sample A .0110 .0278 Descriptions of Samples .0532 .0428 .0190 Sample B .0066 .0028 .0008 SDMeans of Meansof Means Interval49.988 1.029 49.917Ordinal 1.026 Percentile 49.408 7.379 Interval49.997 1.027 50.033Ordinal 1:027 Percentile 50.226 7.461 MeanSD of ofSDs SkewsSDs 0.0200.7203.806 0.0140.5153.830 27.574 0.0213.523 0.9781.1023.709 0.6110.7943.780 27.675 0.0043.447 SDMean of ofKurtosisSkews Kurtosis -0.375 0.7810.520 -0.971 0.4640.367 -1.045 0.4250.381 0.4950.5931.679 -0.409 0.4841.131 -1.060 0.4320.389 TABLE B - 26 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS Normal (N = 15) andPositive Skewed(N = 15) DISTRIBUTIONS Levels of Significance OF SIGNIFICANCE FOR Int. - Int. A Scales B .0000.0010 .0008.0050 .0028.0100 ,0090.0250 .02341".0500 .0994*.0500 .0694*.0250 .0402*.0100 .0300*.0050 ..11122-.0010 Int. - Ord. .0004.0000 .0024.0000 .0012 .0056* .0202*.0130* .1166*.1474* .1024*.0706* .0634*.0344 .02180460* ,01EL.0088 Ord.Int. - Per.Int. / .0000.0G00 .0010.0000 ,ffla.0014.0032 AllQ.0064.0090 .0136*.0234* ,42118,.1436* .1000*.0688* .0616*.0386* .0452*.0294* .0192.0116 Ord.Per.Ord. - -Ord. Int.Per. .0002.0004 .0024.0050 .0048.0098 .0214.0118 .0476.0210* .0546.1154* .026B.0686* .0354*.0114 .0052.0216 .0010.0088 Nc:r%w : Per. - Ord. .0004 .0034 .0068 .0160 .0340 .0698* .0356 .0180 .0080 .0016 Per. - Per. .0004 .0012 Sample A .0036 .0122 Descriptions of Samples .0226* .0826* .0446* Sample B .0202 .0110 .0032 SDMeans of Meansof Means Interval50.002 1.016 49.940Ordinal 1.016 Percentile 49.542 7.303 Interval50.043 5.134 48.404Ordinal 4.223 Percentile 46.383 7.824 MeanSD of,of SkewsSDs -0.004 0.7253.786 -0.002 0.5213.819 27.485 0.0063.556 18.553 0.9995.574 15.511 0.8023.457 29.203 0.0723.616 SDMean of ofKurtosisSkews Kurtosis -0.372 0.5230.778 -0.959 0.3720.484 -1.040 0.3830.438 0.6101.7690.543 0.0200.4941.218 -1.085 0.4390.389 TABLE B - 27 OBTAINED PERCENTAGES OF t VALUES FOR Normal (N = 15) andPositive Skewed(N = GIVEN LEVELS OF SIGNIFICANCE 15) DISTRIBUTIONS FOR A Stales B .0010 .0050 .0100 .0250 Levels of Significance .0500 .0500 .0250 .0100.0300* .0050.0198 .0010.0086 Int.Int. - -Int. Ord. .0004.0000 .0018.0016 .0040.0026 .0148.0106 .0353.0304* .0738*.0840* .0456*.050* .0276.0102 .0162.0066 .0028.0062 Ord.Int. - -Int. Per. .0026.0000 .0096.0020 .0036.0168 .0346.0118 .0314.0612 .0716*.0810*.0444 .0450*.0532*.3224 .0254.0278 .0154.0176 .00840056 Ord.Ord. - -Ord. Per. .0030.0006 .0104.0024 .0182.0046 .0354.0152 .0360.0466.0654 .0546.0416 .0300.0216 .0152.0104 __- .0086.0060 .0026 = 1 Per. - Int. .0012 .0040 .0070 .0224 vrs., Per.Per. - -Ord. Per. .0024.0014 .0066.0050 .0084.0126 .0242.0332 .0640.0520 .0506.0404 .0196.0283 .0100.0142 .0054.0080 - .0012.0024 interval tardinaiSample A Percentile Descriptions of Samples Interval OrdinalSample B Percentile 50.216 MeansMeanSD of of ofMeans MeansSDs 50.000 3.8181.043 49.933 3.8357.041 49.837 2.4989.203 50.004 7.3612.090 50.133 7.4112.104 9.1692.494 MeanSD of ofSDo Skews 0.7310.009 0.5240.007 0.0151.194 0.6030.9752.237 2.1040.5960.936 -0.021 0.3851.211 MeauSDSD of ofSkews Kurtosis -0.383 0.7760.514 -0.963 0.4830.375 -1.038 0.4420.386 0.4811.739 1.6930.152 -1.044 0.432 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE TABLE B - 28 FOR A Scales B .0010 .0050 Normal .0100 (N =15 ) andPositive Skewed(N = 15) .0250 Levels of Significance .0500 .0500 .0250 DISTRIBUTIONS .0100 .0050 .0010 Int. - Ord.Int. .0004 _0024.0016 .0042.0030 ,1152..0132 .0338.10308 .0700*.0852* .0450*.0518* .0320*.0246 .0194 .0044.0064 Ord.Int. - -Int. Per. .0004.0018 jliggt.0020 .0038.0136 .0140.0310 .0306*.0570 .0404.0780* .0206.0494* .0284.0078 Anza-Lusa.0194 .0006.0054 Ord. - Ord.Per. .0004.0024 .0072.0024 .0146.0054 .0330.0156 .0618.0358 .0376.0666 .0168.0406 .0062.0244 .0030.0138 .0006.0040 coIVw 1 Per. - Ord.Int. .0004 .0028.0018 .0054.0042 .0170.0140. .0382.0324 .0622.0720* .0364.0432 .0196.0232 .0122.0154 .0030 Per. - Per. .0020 Interval .0076 OrdinalSample A .0130 Percentile.0360 Descriptions of Samples .0654 .0356 Interval .0164 OrdinalSample B .0050 Percentile .0026 .0008 MeansSD of of Means Means 49.982 1.037 49.912 1.031 49.897 1.237 50.031 2.085 50.161 2.083 50.107 4.6001.237 MeanMeanSD of ofSDsSDs Skews -0.002 0.7293.817 0.5150.0043.834 0.0140.5834.596 0.9812.2517.434 0.9502.1317.499 -0.018 0.586 MeanSD of SkewsKurtosis -0.370 0.5190.758 -0.966 0.4610.371 -1.045 0.3810.415 0.4850.6011.726 0.1850.6001.718 -1.050 0.4190.383 B - 29 OBTAINED PERCENTAGES OF t VALUES Normal (N =30 ) andPositive TABLE FOR GIVEN Skewed(N LEVELS OF SIGNIFICANCE =30 ) DISTRIBUTIONS FOR A Scales B .0010 .0050 .0100 .0250 Levels of Significance .0500 .0500 .0250 .0100 .0050 .0010.0014 Int.Int. - -Int. Ord. _nom.0000 .0020.0016 Asilak_ono Ala.0112 Alm.0374 .0430.0630.n747* A428 .0182.0372 .0180.0214.0072 .0024.0112.0134 .0030.0006 Ord.Int. - -Int. Per. .0026.0000 _0020.0080 ,0124.0050' .0136.0314 ,0574 .0336 .0574.0688 .0328.0390 .0162.0200 .0104.0120 .0024.0030 Ord. - Per.Ord. .0000.0024 .0086.0028 .0158.0062 .0174.0356 .0640.0430 .0646.0368 .0158.0360 :0170.0064 .0096.0024 10018.0006 m 1 Per. - Int. .0000 .0018 .0054 .0140 .0370 .0022 r.3..o Per. - Ord.Per. .0002 0022 .0086.0030 .0146.0064 .0174.0358 .0660.0460 .0366.0542 .0300.0150 .0060.0140 .0070.0024 .0004 Interval OrdinalSample A Percentile Descriptions of Samples Interval 50.014 OrdinalSample50.138 B Percentile 50.096 MeansMeanSD of of ofMeans MeansSDs 50.007 0.7293.893 49.941 0.7323.908 0.87849.9294.669 7.7341.444 7.7671.439 0.8724.695 MeanSD of SDsSkews -0.001 0.499 -0.002 0.346 0.0080.392 1.6640.5851.250 1.5660.5801.174 -0.0110.4030.267 MeanSDSD of ofSkews Kurtosis -0.202 0.3970.673 -1.018 0.2640.321 -1.107 0.254.0.269 2.4641.561 2.3641.132 -1.112 0.258 30 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR Normal (N = 5 ) andPositive Skewed(NTABLE =B 15) DISTRIBUTIONS Int. - int. A Scales B .0002.0010 .0014.0050 .0034.0100 .0126.0250 Levels of Significance .0324.0500 .0788.0500 * .0470*.0250 .0240.0100 .0134.0050 .0044.0010 Int. - Per.Ord. .0000 .0002.0020, .0004.0038 .0014*.0148 .0046*.0352 .0064*.0610 .0332.0020* .0002.0142 .0000.0082 .0024 Ord. - Ord.Int. .0002 _M20.0026 .0046.0042 .0194.0174 .0402.0358 .0598.0748* .0318.0460* .0148.0244 .0142.0084 .0030.0148.0000 Per.Ord. - Int.- Per. .0536*.0000.0002 .0804*.0002 .1036*.0004 .1396*.0014* .0046*.1834* .1620*.0060* .1258*.0020* .0910*.0002 .0738*.0000 .0510*.0000 0w Per. - Per.Ord. .0012.0542* .0048.0818* .0098.1038* .0232.1398* .0472.1842* .0468.1608* .0216.1240* _.0906*.0088 .0736*.0034 .0006.0504* Interval OrdinalSample A Percentile Descriptions of Samples Interval49.976 50.007OrdinalSample B Percentile 49.998 MeanSDMeans of ofofMeans SDsMeans 50.001 3.3641.720 49.940 1.7193.441 24.82612.35949.555 1.0363.711 3.7871.032 27.693 7.456 MeanSD of SDsSkews -0.004 1.204 -0.004 0.981 6.8230.002 0.9881.122 0.6280.808 0.3910.0163.513 MeanSD of KurtosisSkewsKurtosis -1.000 0.6110.501 -1.047 0.5891.728 -1.119 0.5160.583 0.5290.6091.770 -0.371 0.4971.216 -1.060 0.439 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR TABLE B - 31 A Scales B .0010 .0050Normal .0100 (N = 5 .0250 ) andPositive Skewed(N =15 ) Levels of Significance .0500 .0500 .0250 DISTRIBUTIONS .0100 .0050 .0010 Int. - Int. .0008 .0024.0026 .0072.0064 .0184.0176 .0422.0396 .0782*.0596 .0344.0428 .0150.0246 .0090.0148 .0030.0056 Ord.Int. - -Int. Per.Ord. .0010.0000.0008 .0036.0008 .0074.0020 .0218.0042* .0470.0108* .0712*.0118* .0430.0040* .0236.0018 .0152.0010 .0058.0002 Ord.Ord. - -Ord. Per. .0010.0000 .0008.0036 .0022.0086 .0042*.0232 . .0486.0122* .0116*.0568 .0348.0040* .0168.0014 .0010.0094 .0004.0030 t r. Per. - Int. .0290* .0544* .0720* .1046* .1430* .1330* .0956* .0678* .0534* .0264* Per. - Per.Ord. .0014.0282* .0552*.0056 .0112.0734* .0292.1052* .0534.1450* .0468.1310* .0244.0938* .0104.0628* .0486*.0048 .0014.0244* Means of Means Interval 50.022 OrdinalSample49.952 A Percentile 49.878 Descriptions of Samples Interval 50.003 OrdinalSample50.031 B Percentile. 50.053 SD of Means -. 1.798 3.4131.797 8.1974.309 1.0303.736 3.8001.028 9.2322.467 MeanSD of SDsSkewsSDs 0.0081.2163.342 0.0091.000 0.0102.337 0.9881.123 0.6240.803 .0.0151.170 SDMean of ofSkewsKurtosis Kurtosis -1.002 0.5080.613 -1.067 0.8070.596 -1.117 0.5180.586 1.7270.5120.602 -0.395 1.1690.486 -1.067 0.4290.385 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE TABLE B - 32 FOR A Scales B .0010 .0050 Normal .0100 (N = 5 ) andPositive Skewed(N =15 ) .0250 Levels of Significance .0500 .0500 .0250DISTRIBUTIONS .0100 .0050 .0010 Int. - Ord.Int. .0004.0002 .0030.003, .0054.0052 .0152.0160 .0390.0334 .0560.0746* .0298.0424 .0124.0220 .0120 .0044.0022 Ord.Int. - Per.Int. .0008.0004 .0034.0024 .0074.0040 .0176.0130 .0416.0340 .0738*.0288* .0136.0410 .0052.0218 ,0022.0078.0134 .0052.0000 Ord. - Per.Ord. .0006.0008 .0022.0036 .0058.0070 .0174.0196 .0364.0450 .0562.0276* .0126.0294 .0044.0134 -.0024.0072 .0000.0022 m 1 Per. - Int. .0026 .0078 .0138 .0324 .0658 .0862* .0512* .0268 .0174 .0076 ts.)i...i Per. - Ord. .0022 .0074 . .0146 .0362 .0678 .0732* .0416 .0190 .0116 .0046 Per - Per. .0008 .0046 Sample A .0104 .0278 Descriptions .0540 of Samples .0434 .0194 Sample B .0086 .0042 .0010 MeansSD of of Means Means Interval49.995 1.776 49.934Ordinal 1.781 Percentile 49.920 2.140 Interval50.002 1.033 Ordinal50.036 1.028 Percentile50.050 1.235 MeanSD of SDsSkews -0.009 1.2083.379 -0'005 0.9873.448 0.0001.1564.144 0.9811.1053.699 0.6150.7953.773 0.5844.5960.005 SDMeanSD of of Kurtosis SkewsKurtosis .---f6.996 0.5080.616 -1.075 .558.600 -1.104 0.5960.524 1.7290.5100.603 -0.397 0.4821.154 -1.068 0.4270.379 TABLE B 33 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN Normal (N =15) and Positive Skewed(N LEVELS OF SIGNIFICANCE =30 ) DISTRIBUTIONS FOR Int. - Int. A Scales B .0000.0010 .0Q16.0050 .0058.0100 .0250 Levels of Significance .0398.0500 -0846*.0500 .0250 .0100Jp(14 -L128.0050 -01148.0010 Int.Int. - -Ord. Per. .000 .0028.0024 ..2u1.0080 A212,.0206.0180 .0444 0484 ..0408,Jmn -Ma.0178_014R .0072,_nittn _Dna.0030 .0006 00 24 Ord.Ord. - Int.- Ord. _MIL.0004.0006 .0040.0024 .0084.0062 .0260.0216 .0548.0480 .0650.0540 .0316.0388 .0122.0174 .0076.0104 .0024.0038 Ord.Per. - -Per. Int. .0008.0006 .0036.0058 '.0084 .0124 .0302.0258 .0608.0478 .0712*.0384 .0154.0436 .0060.0210 .0132.0028 .0044.0008 wm i Per. - Ord. .0010 .0070 .0158 .0352 .0670 .0624 .0362 .0078.0162 .0088.0048 .0012.0032 Per. - Per. .0010 Interval .0058 OrdinalSample A.0122 Percentile.0316 Descriptions of Samples .0616 .0460 Interval .0240 OrdinalSample B Percentile MeansSD of of Means Means 50.007 1.038 49.947 1.032 49.933 1.237 49.998 0.744 50.032 0.741 50.036 4.7040.886 MeanMeanSD of ofSDs Skews -0.002 0.7283.817 -0.005 0.5183.834 0.0030.5894.595 1.2240.8453.853 0.7230.5953.888 0.0040.401 MeanSDSD of of Skews KurtosisKurtosis -0.362 0.7810.526 -0.964 0.4780.370 -1.045 0.4320.380 2.5031.5220.598 -0.047 0.4661.634 -1.137 0.2510.268 OBTAINED PERCENTAGES OF t Normal (N =5 VALUES FOR GIVEN) andPositive LEVELS OF Skewed(N SIGNIFICANCETABLE =B 15)- 34 FORDISTRIBUTIONS Int. - Int. A Scales B .0010 .0000.0050 .0000.0100 .0004*.0250 Levels of Significance .0006*.0500 .0296*.0500 .0138.0250 Apia.0100 .0040.0050 ' .211.0010 Int. - Ord. ANQ .0000 .0006* .0410 .0216, .0104 .0058 ' ,0016 Ord.Int. - -Int. Per. -ono .0000 .0000.0002 A00I2.0000.0002 ADO,.0004*.0006* .0008*.0016* .0276*.0154* .0060 .0074.0024 .0042.0012 .0002,.0008 Ord.Ord. - -Ord. Per. ,OQQQLQQQQ .0002.0000 .0000.0002 .0008*.0002* ,00,.0020* .0150*.0400 ,QIii.0062.0210 .0026.0096 .0054.0012 .0002.0014 to i Per. - Int. .0062 .0186 .0266 .0480* .0834* .1024* .0646* .0386* .0270* .0104 4...) .c. Per. - Ord. .0080 .0206 .0296* .0530* .0878* .1282*' .0856* .0144.0546* .0400*.0074 .0168.0014 Per. - Per. .0004 Interval .0030 OrdinalSample A .0040 Percentile.0124 Descriptions of Samples .0276* .0628 Interval .0350 OrdinalSample B Percentile MeanSDMeans of ofMeansof SDs Means 50.027 1.7533.348 49.964 3.4201.763 12.67449.73724.687 50.05318.337 5.248 48.52515.521 4.296 46.64329.135 7.935 MeanSD of ofSDs Skews -0.010 1.231 -0.011 1.007 -0.005 7.033 0.5980.9795.507 0.5000.8053.475 0.3850.0593.626 MeanSDSD of of Skews KurtosisKurtosis -1.001 0.6130.500 -1.063 0.5940.912 -1.112 0.5900.518 1.7010.491 1.2320.051 -1.082 0.421 TABU: B - 35 OBTAINED PERCENTAGES OF t VALUES FOR Normal (N =5 ) and Positive GIVEN LEVELS Skewed(N OF.15 SIGNIFICANCE ) DISTRIBUTIONS FOR Int. - Int. A scales B .0010.0000 .0000.0050 .0000.0100 .0250.0004* Levels of Significance .0500.0044* .0500.0462 .0250.0252 .0100.0124 .0064.0050 .0010.0006 Int. - Per.Ord. .0002.0000 .0008.0000 .0008.0002 .0034*.0008* .0124*.0050* .0100*.0380 .0026*.0218 .0004.0094 .0004.0046 .0000.0010 Ord. - Ord.Int. .0000.0000 .0000 .0002.0000 .0014*.0010* .0050*.0046* .0440.0376 .0216.0246 .0078.0106 .0042.0060 .0008.0010 to Ord.Per. - -Per.' Int. .0028.0000 .0008.0098 .0154.0008 .0328.0038* .0144*.0586 .0842*.0082* .0534*.0020* .0294*.0004 .0188.0004 .0076.0000 %.nL.) i Per. - Ord. .0008.0026 .0050.0098 .0096.0148 .0288.0330 .0502.0608 .0458.0806* .0484*.0204 .0268.0084 .0044.0178 .0008.0068 Per. - Per. Interval OrdinalSample A Percentile Descriptions of Samples Interval OrdinalSample B Percentile MeansSD of of Means Means 50.027 1.753 49.964 1.763 49.912 4.225 49.977 2.090 50.101 2.087 50.147 9.1652.502 MeanSD of SDsSkews -0.010 1.2313.348 -0.011 1.0073.420 -0.0058.2292.344 1.0042.2687.408 0.9622.1337.462 -0.003 1.180 SDMean of ofKurtosisSkews Kurtosis -1.001 0.6130.500 -1.063 0.9120.594 -1.111 0.5180.590 1.8010.5530.613 1.7660.2160.608 -1.050 0.4240.380 OBTAINED PERCENTAGES OF t VALUES TABLE FOR GIVEN LEVELS B - 36 OF SIGNIFICANCE FOR Scales B .0010 .0050Normal .0100 (N =5 ) and .0250 LevelsPositive of Significance Skewec(N .0500 .0500 =15 ) .0250DISTRIBUTIONS .6100 .0050 .0010 Int. - Ord.Int. A .0000 .0000 .0000 .0012*.0004* .0044*.0050* .0434.035; .0212.0164 .0090.0078 .0044.0056 A018.0012 Ord.Int. - Int.Per. .0000.0004 .0000.0026 AE8Ago.0000 .0176.0008* ,0374'.0060* .0420.0274* .0198.0120 .0098.0046 .0024.0056 .0018.0002 Ord.Ord. - -Ord. Per. .0004.0000 .0032.0000 .0082.0002 .0190.0010* .0064*.0404, .0344.0266* .0162.0124 .0042.0080 .0022.0052 .0004.0014 w I Per. - Int. .0000 .0000 .0000 .0028* .0116* .0480 .0244 .0120 .0076 .0018 t...1 Per. - Ord. .0000 .0000 .0004 . 0126* .0404 .0186 . .0062 .0018 ch Per. - Per.. .0010 .0074 Sample A .0136 _me.0280 Descriptions of Samples .0562 .0438 .0196 80088Sample B .0068 .0038 .0012 MeansSD of of Means Means Interval50.007 1.802 49.946Ordinal 1.803 Percentile 49.936 2.162 Interval50.008 2.060 50.140Ordinal 2.069 Percentile50.102 1.235 MeanSD of SDsSkewsSDs -0.001 3.3361.209 -0.003 0.9893.409 0.0001.1524.098 0.9912.2187.407 0.9542.1157.472 -0.018 0.5864.591 MeanSD of KurtosisSkewsKurtosis -0.990 0.6200.501 -1.073 0.5540.602 -1.100 0.5260.600 1.7370.5250.609 1.7130.2030.604 -1.037 0.4420.389 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR TABLE B - 37 A Scales B .0010 .0050 Normal .0100 (N = 15) andPositive Skewed(N = 3Q) DISTRIBUTIONS .0250 Levels of Significance .0500 .0500 .0250 .0100 .0050 .0010 Int.Int. - Int.- Ord. .0000 .0004.0002 /.'07006 .0008 .0042*.0030* .0144*.0114* .0370.0442 .0208.0234 .0118 .0058.0066 .0016.0028 Ord.Int. - Int.Per. .0000.0014 .0002.0040 .0008.0086 .0022*.0238 .0120*.0470 ,020.0398 .0234.M66 ,culpMI6ggij .0066.0022 .0020.0002 Ord. - Ord. - Per. .0000.0014 .0042.0004 .0094.0012 .0262.0042* .0504.0154* .0292*.0340 .0154.0194 .0060.0078 .0022.0060 .0000.0014 Per.Ord. - Ord.Int. .0000.0000 .0008.0006 .0014.0012 .0062.0048* .0216*.0178* .0378.0450 .0252.0218 .0120.0098 .0062.0064 .0020.0026 Per. - Per. .0018 .0076 Sample A .0130 .0332 Descriptions of Samples .0612 .0378 .0190 Sample B .0080 .0046 .0010 MeansSD of of Means Means Interval49.988 1.031 49.922Ordinal 1.027 Percentile 49.907 1.231 Interval49.966 1.441 50.094Ordinal 1.443 Percentile50.086 0.874 MeanSD of SDsSkews 0.0040.7323.802 0.0030.5243.830 0.0140.5984.594 1.2311.6737.647 1.1571.5587.682 -0.015 0.4104.685 SDMean of ofKurtosisSkews Kurtosis -0.393 0.7600.507 -0.974 0.4640.363 -1.050 0.4100.374 2.3831.5110.578 0.5752.3051.082 -1.108 0.2580.268 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR TABLE B 38 A Scales .0010 .0050Normal .0100 (N 15) andPositive.0250 Skewed(N Levels of Significance .0500 .0500 5) DISTRIBUTIONS .0250 .0100 .0050 .0010 Int.Int. - -Ord. Int. .0098.0132 .0266*.0318* _0176*.0490* _01R0*.0580* .0848* .2976*.2564* .2548*.2180* .1736*2010* .1676*.1444* .1132*.1004* Ord.Int. - -Int. Per. .0390*.0130 .0318*.0600* .0488*.0718* .0790*.0924* .1192*.1228* .2594*.2630* .2164*.2340* .1702*.1634* .1434*.1350* .0976*.0902* Ord.Ord. - -Ord. Per. .0386*.0102 .052i*.0266* .0724*.0382* .0938*.0588* .1236*.0870* .2602*.2966* ,2116*.2526* .1632*.1976* .1342*.1664* .0890*.1114* Per.Per. - -Ord. Int. .0000.0002 _10010 .0024 .0014.0040 .0034*.0100 .0118*.0226* .0176*.0166* .0078.0074 .0026.0020 .0014.0012 .0000.0000 Per. - Per. .0008 .0032 Sample A .0048 .0158 Descriptions of Samples .0340 .0798* .0406 Sample B .0198 .0100 .0022 SDMeans of Meansof Means Interval49.992 1.026 49.924Ordinal 1.026 Percentile 49.452 7.373 Interval 50.018 9.058 Ordinal48.274 7.385 Percentile 13.65545.996 MeanSD of SDsSkews! -0.000 0.7183.825 0.0020.5143.841 27.653 0.0133.522 16.124 0.4618.387 13.611.0.3985.821 26.302 0.0657.320 SDMean of ofSkewsKurtosis Kurtosis -0.371 0.7920.519 -0.967 0.4730.372 -1.044 0.4290.382 -0.907 0.5780.592 -0.940 0.5670.596. -1.110 0.5270.599 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR TABLE B - 39 A Scales B .0010 .0050 Normal .0100 (N =15 ) andPositive Skewed(N =5 .0250 Levels of Significance .0500 .0500 ) DISTRIBUTIONS.0250 .0100 .0050 .0010 Int. - Ord.Int. .0066.0044 .0182.0150 .0276.0256 .0564*.0486* .0918*.0848* .1444*.1574* .1012*.1084* .0628*.0636* .0444*.0442* .0186.0156 Ord.Int. - -Int. Per. .0042.0256* .0152.0512* .0254.0670* .0514*.1002* .0882*.1412* .1498*.1298* .1026*.0908* .0588* .0380*.0432* .0116.0214* Ord. - Per.Ord. .0250*.0058 .0520*.0178 .0696*.0288 .1042*.0580* .1450*.0942* .1270*.1402* .0880*.0962* .0570*.0582* .0424*.0406* .0204*.0140 ..7. 1 Per. - Int. .0002 .0032 .0056 .0174 .0374 .0290* .0134 .0038 .0022 .0006 s.0(....) Per. - Ord. .0002 .0032 .0062 .0178 .0376 .0278* .0134 .0034 .0020 .0004 Per. - Per. .0012 .0074 Sample A .0124 .0294 Descriptions of Samples .0582 .0440 .0230 Sample B .0088 .0034 .0002 SDMeans of Meansof Means Interval50.003 1.043 49.939Ordinal 1.035 Percentile 49.853 2.482 Interval50.010 3.596 50.134Ordinal 3.577 Percentile 50.150 4.277 MeanSDMean of ofSDsSkews SDs -0.002 0.7343.822 /-0.002 0.5223.839 0.0061.1869.198 0.4536.4423.379 0.5163.1886.502 0.0022.3268.297 MeanSD of KurtosisSkews -0.371 0.7750.528 -0.965 0.4760.375 -1.048 0.3800.414 -0.911 0.5800.593 -1.652 0.620 .882 -1.104 0.5210.594 TABLE B - 40 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE Normal (N =15 ) andPositive Skewed (N =5 ) DISTRIBUTIONS FOR Int. - Int. A Scales B .0044.0010 .0169.0050 .0262.0100 ,0518*.0250 Levels of;Significance .0500 .1530*.0500 .1040*.0250 .0656*.0100 :0442*.0050 .0166.0010 `Int. - Per.Int. - Ord. _.0062 .0126.0186 .0226.0306* .0446*.0604* jas.0924*.0750* .0650.1416* .0344.0978* .0638*.0170 .0440* .0026.0186 Ord. - Ord.Int. .0060.0050.9048 .0196.0158 .0314*.0276 .0622*.0530* ADO!.0944* .1440*.1344* .0938*.0988* .0598*.0592* Jaz.0422*.0390* .0150.0124 co Per.Ord. - Int.- Per. .0028.0038 .0138.0126 .0216.0214 .0448*.0452* .0760*.0778* .1158*.0608 .0728*.0322 .0364*.0150 .0202.0076 .0016.0048 o.c- 1 Per. - Per.Ord. .0016.0046 .0142.0076 .0142.0242 _.0312.0510* .0584.0882* .0424.1110* .0692*.0208 .0074.0368* .0040.0198 .0008.0058 Interval OrdinalSample A Percentile Descriptions of Samples Interval 50.028 Ordinal50.157Sample B Percentile 50.099 MeanSDMeans of of Meansof SDs Means 50.001 1.0333.801 49.937 1.0353.826 49.923 1.2404.591 6.4313.557 6.5073.553 4.1562.125 MeanSD of SDsSkews -0.004 0.724 -0.000 0.523 0.5930.3850.006 0.5930.4473.310 0.6150.5093.167 -0.002 0.5911.166 SDMean of ofKurtosisSkews Kurtosis -0.372 0.5230.794 -0.959 0.3760.491 -1.038 0.431 -0.922 0.583 -1.461 .970 -1.106 0.862 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS TABLE B 41 OF SIGNIFICANCE FOR A Scales B .0010 Normal.0050 .0100 (N =30) andPositive Skewed(N =15 ) .0250 Levels of Significance .0500 .0500 .0250DISTRIBUTIONS .0100 .0050 .0010 Int.Int. - Int.- Ord. .0014.0016 .0074 .0157filan .0178 _papa*.0714* _113a*-120* 0779*0857* 0474*0450* _nun* 0147n152 Ord.Int. - -Int. Per. .0012.0026 _am.0076.0090 .0168_niqn _nun.0406.04Q4 .0740*A1794* .1-08*-n514 _man.0810* _mAn.0446* -QOM.0316*DM* .0134 OMB Ord. - Per.Ord. .0032.0014 .0102.0090 .0194.0210 .0410.0444* .0792*.0832* .0472.1270* .0254.0684* .0128.0382* .0074.0264* .0138.0018 .".tv2 Per. - Ord.Int. .0012.0014 .0088.0060 .0160.0130 .0410.0344 .0766*.0692* .0914*.1232* .0620*.0538* .0272.0316* .0182.0208 .0082.0096 Per. - Per. .0016 .0068 Sample A .0142 .0340 Descriptions of Samples .0636 .0392 .0190 Sample B .0088 .0050 .0010 MeansSD of of Means Means Interval50.001 0.739 49.939Ordinal 0.737 Percentile 49.925 0.884 Interval50.020 2.064 Ordinal50.147 2.069 Percentile 50.101 1.235 MeanMeanSD of ofSDsSDs Skews -0.002 0.5173.903 -0.000 0.3593.912 0.0080.4034.689 1.0012.2667.437 0.9632.1457.492 -0.014 0.6014.591 MeanSDSD of of Skews Kurtosis -0.186 0.7010.408 -1.012 0.3430.267 - 1.108. 0.2670.270 1.7670.5500.608 0.2290.6041.750 -1.047 0.4320.377 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR TABLE B - 42 A Scales .0010 .0050Normal .0100 (N = 5 ) andNegative Skewed(N = 5 ) .0250 Levels of Significance .0500 .0500 .0250DISTRIBUTIONS .0100 .0050 .0010 Int. - Ord.Int. .0034.0040 .0094.0122 .0218 .0348.0416 .0612.0720* .0420.0336 .0132 .0070.0042 .0030,.0020 .0008.0002, Ord.Int. - -Int. Per. .0048.0104 ,0178.0152 Aim.0228.0254 .0418,.0414 46118.0732* ,2312..0766* sun.0162.0520* .0054.0284 .0026.0206 .0002.0084 Ord. - Per.Ord. .0104.0036 .0184.0104 ADA.0258 .0420.0354 .0678.0624 .0766*.0416 .0199, .0286.0074 .0200.0038 .0084.0006 Per. - Ord.Int. .0102.0106 .0212.0218 .0304*.0 06* .0478*.0482* .0694*.0704* fthA 051e.0424.0418 .0262.0260 .0194.0188 .0088.0084 Per. - Per. .0024 .0066 Sample A .0112 .0272 Descriptions of Samples .0524 ..01,51.0532 .0284 Sample B .0124 .0078 .0030 SDMeans of Meansof Means Interval49.999 1.769 49.939Ordinal 1.769 Percentile 12.70949.565 Interval49.996 1.788 Ordinal49.935 1.776 Percentile 12.89649.486 MeariMeanSD ofof SDsSDsSkews -0.010 1.2103.352 -0.008 0.9963.425 -0.00524.705 6.954 -0.426 1.6143.197 -0.300 1.2563.317 24.848 0.0136.848 SDMean of ofSkewsKurtosis Kurtosis -0.996 0.5170.617 -1.073 0.9380.595 -1.111 0.5190.591 -0.926 0.5970.602 -0.952 1.5000.608 -1.113 0.5330.603 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR TABLE B - 43 Scales B .0010 .005 Normal .0100 (N 5 ) andNa gative.0250 Skewed(N Levels of Significance .0500 .0500 5 ) DISTRIBUTIONS.0250 .0100 .0050 .0010 Int. - Int. A .0024.0032 .0114.0144 .0244.3198 .0390.0464* .0646.0760* .0420.0324 .0184.0134 .0074.0048 .0040.0018 .0012.0004 Int. -.Per.- Ord. .0058.0044 .0146.0144 .0254.0194 .0460*.0362 .0754*.0562 .0308.0706* .0140.0424 .0052.0220 .0030.0152 .0004.0072 Ord.Ord. - -Ord.Int. Per. .0066.0032 .0142.0118 .0188.0204 .0374 .0658.0570 .0682.0400 .0418.0184 .0212.0074 .0146,0044 .0070.0012 to Per. - Ord.Int. .0054.0058 .0148.0160 .0208.0234 .0414.0446* .0702.0718* .0582.0566 .0346.0328 .0184.0174 .0106 .0038 Per. - Per. .0010 .0074 Sample A .0156 .0282 Descriptions of Samples .0536 .0568 .0278 Sample B .0114 .0070 .0024 SDMeans of Meansof Means Interval49.999 1.763 49.938Ordinal 1.767 Percentile 49.846 4.243 Interval49.930 1.814 Ordinal49.873 1.788 Percentile 49.716 4.272 MeanSD of SDsSkewsSDs 0.0041.2093.346 0.9903.4270.003 8.2370.0112.312 -0.425 1.6933.257 -0.301 1.3233.362 0.0212.3548.330 SDMean of ofSkewsKurtosis Kurtosis -1.000 0.5050.612 -1.078 0.7560.596 -1.109 0.5210.591 -0.921 0.6300.610 -0.862 2.8700.610 -1.111 0.5300.600 TABLE B - 44 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN Normal (N = 5 ) andNegative Skewed(N = S ) LEVELS OF SIGNIFICANCE FOR DISTRIBUTIONS Int. - Int. A Scales B .0228*.0010 .0500*.0050 .0712*.0100 .1038*.0250 Levels of Significance .1438*.0500 .0228*.0500 .0094.0250 .0034.0100 .0050.0018 .0006.0010 Int. - Ord.Per. .0124.0236* .0276*.0548* .0764*.0384* .0630*.1118* .0932*.1544* .0224*.0536 .nnm.0102 .0200.0034 .0020.0142 .0008.0064 Ord. - Int.Ord. .0224*.0222* .0516*.Q558* .0704*.0788* .1132*.1072* Jab,.1570* .0178*.0220* .0100.0094, Ma.0034 .0018.0016 .0004.0006 os Per.Ord. - Per.Int. .0052.0126 .0272*.017f; .0254.0398* _,0638*.0450 * .Q730.0936* * .0424.0534* .0316*.0222 .0092.0194 .0146..0050 .0062.0018 .c..c.- o Per.Per. - -Ord. Per. .0026.0060 .0166.0176 .0166.0258 .0398.0462* .0762*.0726* .0370.0414 .0188.0210 .0114.0086 .0062.0048 .0018.0020 Interval SampleOrdinal A Percentile Descriptions of Samples Interval OrdinalSample51.231 B Percentile 52.855 MeansMeanSD of of ofMeans MeansSDs 50.019 1.7943.377 49.956 1.7903.435 49.66924.74512.841 50.08016.0238.870 13.548 7.294 26.30913.506 MeanSD of ofSDs Skews -0.011 1.238 -0.010 0.998 -0.008 6.962 -0.440 8.3060.605 -0.3765.7050.611 -0.022 0.6047.173 SDMean of ofSkewsKurtosis Kurtosis -0.991 0.5090.621 -1.062 0.8890.601 -1.1u4 0.5260.596 -0.916 0.589 -1.354 .922 -1.113 0.536 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR TABLE B - 45 Scales Normal (N = 5 ) andNegative Skewed(N = Levels of Significance .0500 5 ) DISTRIBUTYNS .0250 .0100 .0050 .0010 Int. - Ord.Int. A B .0068.0114.0010 .0286*.0228.0050 .0358*.0434*.0100 .0690*.0670*.0250 .1028*.1034*.0500 .0234*.0260* .0092.0100 .0040.0032 .0014.0020 .0008.0002 Ord. - Int. - Per. .0052.0044 .0222.0128 .0358*.0194 .0654*.0364 .1046*.0618 .0602.0240* .0088.0354 .0034.0190 .0012.0124 .0004.0030 Ord.Ord. - -Ord. Per. .0040.0082 .0120.0270* .0196.0404* .0370.0684* .0634.1054* .0594.0252* .0342.0104 .0036.0184 .0122.0020 .0032.0006 to Per. - Int.Ord. .0046.0048 .0124.0132 .0208.0200 .0376 .0698*.0686 .0390.0410 .0152.0164 .0064.0070 .0042.0038 .0018.0014 Per. - Per. .0018 .0058 Sample A .0118 .0312 Descriptions of Samples .0538 .0436 .0246 Sample B .0106 .0048 .0026 MeansSD of of Means Means Interval 50.032 1.783 Ordinal49.964 1.787 Percentile 49.913 4.275 Interval 50.028 3.587 Ordinal50.114 3.495 Percentile 50.084 4.313 MeanMeanSD of ofSDs Skews - 0.001 1.2473.355 -0.011 1.0173.418 -0.002 2.3558.220 -0.441 3.2856.384 -0.508 3.0396.322 -0.013 8.2942.294 SDMean of ofKurtosisSkews Kurtosis - 1.010 0.6060.510 -1.085 0.5940.642 -1.122 0.5850.523 -0.911 0.6040.584 -1.007 0.6271.112 -1.097 0.5280.602 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE TABLE B - 46 FOR Scales B .0010 Normal .0050 .0100 (N =15 ) andNegative Skewed(N =15 ) .0250 Levels of Significance .0500 .0500 .0250 DISTRIBUTIONS .0100 .0050 .0010 Int.Int. - Int.- Ord. A .0018.0030 .0064.0092 .0126.0170 ,0384 -06216. .0328.0418 .0132 .0096.0042 .0022.0034 .0008.0002 Int. - Per. .0016 .0076 .0134 Ma.0272 -DU&.0546 ' .0616 Alm.0138 .0096 .0030 Ord. - Int.Ord. .0020.0038 .0118.0080 .0150.0188 .0296.0400 .0606.0724* .0326.0394 .0172.0126 Alik.0040.0052 .0032.0020 .0010.0006 el Per.Ord. - Int.Per. .0030.0016 .0084.0068 .0136.0170 .0286.0338 .05480642 .0460.0604 .0252.0332 .01240154 .0078.0096 .0030.0024 oN.c. Per. - Per.Ord. .0014.0028 .0052.0084 .0096.0174 .0274.0334 .0526.0642 .0468.0458 .0228.0256 .0120.0088 .0044.0080 .0024 Interval OrdinalSample A Percentile Descriptions of Samples Interval50.006 Ordinal49.946Sample B Percentile 49.591 MeanMeansSD of of Means SDsMeans 49.993 1.0333.795 49.930 3.8181.033 27.49549.491 7.413 3.7161.049 3.7491.040 27.542 7.527 MeanSD of ofSDs Skews 0.0020.722 0.0020.522 0.0113.565 -0.993 0.6021.122 -0.621 0.8050.485 0.3900.0083.434 SDMean of ofKurtosisSkews Kurtosis -0.358 0.5260.787 -0.956 0.3750.469 71.033 0.4270.387 0.5451.720 -0.384 1.154 -1.057 0.434 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LLVELS OF SIGNIFICANCE .FOR TABLE B - 47 Scales B .0010 .0050 Normal .0100 (N =15 ) andNegative Skewed(N =15 ) DISTRIBUTIONS .0250 Levels of Significance .0500 .0500 .0250 .0100 .0050 .0010 Int. - Ord.Int. A .0062.0058 .0170.0166 .0276.0262 .0518*.0528* .0812*.0858* .0276*.0266* .0104.0106 .0034.0036 .0022.0014 .0002.0000 Ord.Int. - -Int. Per. .0060.0020 .0178.0062 .0274.0120 .0520*.0236 .0840*.0488 .0502.0266* .0106.0270 .0120.0036 .0014.0082 .0002.0028 Ord.Ord. - -Ord. Per. .0020.0064 .0062.0184 .0304*.0122 .0254.0532* .0502.0876* .0494.0260* .0098.0258 .0032.0112 .0080.0020 .0028.0002 Per. - Ord.Int. .0044.0038 .0098.0094 .0168.0144 .0336.0322 .0686.0648 .0360.0368 .0178.0178 .0074.0076 .0026.0022 .0006 Per. - Per. .0016 .0058 Sample A .0106 .0260 Descriptions of Samples .0502 .0444 .0216 Sample B .0110 .0052 .0012 MeansSD of of Means Means Interval49.993 1.052 Ordinal49.929 1.049 Percentile 49.826 2.514 Interval 50.000 2.067 Ordinal50.074 2.044 Percentile 50.012 2.461 MeanMeanSD of of SDs Skews -0.001 0.7283.815 -0.000 0.5243.833 0.0109.1981.195 -0.988 2.2207.381 - 7.303-0.949 2.073 -0.0039.1511.195 SDMean of ofSkews Kurtosis Kurtosis -0.368 0.7960.520 -0.954 0.4970.377 -1.031 0.3910.457 1.7240.5220.604 0.1860.5951.686 -1.032 0.4380.389 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF TABLL B - 48 SIGNIFICANCE FOR A Scales B .0010 .0050Normal .0100 (N = 15) andNegatheskeze0Q2LW DISTRIBUTIONS .0250 Levels of Significance .0500 .0500 .0250 .0100 .0050 .0010 Int. - Ord.Int. .0186.0144 .1147n*.0114* A2522!.0424* .0926*.0746* .1402*,1064* .0132*.0222* .0052*.0080 _ftata.0052 .0040.0002 ,0005AIM Ord.Int. - Int.Per. Ana.0150 ..12318!.0164, .0430*.0304* .0754*.0572* ,0276*.0214* .0068.0136 .0008.0066 .0000.0022, ,0002 Ord.Ord. - -Ord. Per. .0060.0204* Qui,.0176 .0310*.0582 * .0576*.0942* .0966*.1408* .0272*.0128* .0136.0048* .0008.0064 .0020.0000 .0002.0000 Per. - Ord.Int. .0016.0010 oam.0090 .0200.0150 .0452*.0324 .0792*.0628 .0298*.0370 .0154.0170 .0072.0078 .0032.0026 .0010.0010, 03 Per. - Per. .0020 ,0076 Sample A.0188 .0470* Descriptions of Samples .0894* .0214* .0122 Sample B .0040 .0022 .0004 MeansSD of of Means Means Interval49.989 1.036 49.926Ordinal 1.025 Percentile 49.446 7.375 Interval 50.025 5.161 Ordinal51.252 4.181 Percentile 52.673 7.757 MeanMeanSD of ofSDs Skews 0.0070.7163.802 0.0040.5113.828 27.536 0.0153.489 -1.00218.424 3.591 -0.80715.215 3.477 -0.03928.817 3.635 MeanSDSD of of Skews Kurtosis -0.380 0.7750.521 -0.969 0.4710.367 -1.047 0.4280.379 0.5610.6171.804 0.0630.5121.277 0.4270.388 B - 49 OBTAINED PERCENTAGES OF t VALUES Normal (N =15) and TABLE NegativeFOR Skewee"N GIVEN LEVELS =15)OF SIGNIFICANCE DISTRIBUTIONS FOR Int. - Int. A Scales B .0068.0010 .0204.0050 .0326*.0100 .0548*.0250 Levels of Significance .0892*.0500 .0500.0308 .0124.0250 .0100.0032 .C310.0050 .0000.0010 Int. - Per.Ord. .0020.0078 .0086.0224 .0136.C34S*' .0298.0c78* .0564.0882* .0540.0304* .0298.0128 .0136.0034 .0078.0014 ...0000.0020 _ Ord.Ord. - -Ord. Int. .0080.0072 .0230.0228 .0354*.0342* .0592*.0576* .0930*.0934* .0264*.0296* .0112.0118 .0036.0030 .0012.0008 .0000 Ord. - Per. .0026 .0102.0086 .0188.0143 .0400.0302 .0670.0578 .0372.0526 .0164.0288 .0066.0136 .0020.0072 .0006.0022 4-..m 1 Per. - Ord.Iut. .0026 .0110 .0200 .0400 .0692* .0362 .0162 .0064 .0022 .0006 Per. - Per. .0016 .0064 Sample A .0124 .0316 Descriptions of Samples .0578 .0460 .0244 Sample B .0112 .0056 .0014 MeansSD of of Means Means Interval50.005 1.030 49.937Ordinal1.028 Percentile 49.846 2.466 Interval50.002 2.069 50.088Ordinal 2.038 Percentile 50.038 2.475 MeanSD of SDsSkews 0.0090.7203.804 0.0060.5123.826 0.0159.1791.169 -0.997 2.2357.410 -0.957 2.0507.317 -0.016 1.1879.171 SDMean of ofKurtosisSkews Kurtosis -0.365 0.8070.529 -0.959 0.4990.377 -1.036 0.3871.448 0.5280.6031.755 1.7390.2080.605 -1.039 0.4400.387 TABU 8 7 50 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS Normal (N = 5 ) andNesatiateskesig OF SIGNIFICANCE FOR DISTRIBUTIONS Scales ' .0010 .0050 .0100 .0250 Levels of Significance .0500 .0500 .0250 .0100 .0050 .0010 Inc.Int. - Int.Ord. A B .0038.0066 .0164 .0260 .0348.0492* .0618.0800* .058.0414 .0166.0134 .nns'.0046 .0026.0020 .0002 Ord.Int. - -Int. Per. .0068.0002 Ano4.sau Jam_nom .0018*.0540* .0844*.0054* .0338.0066* .0142.0014* nnw .0022.0002 .0000.0002 Ord. - Per.Ord. .0002.0046 Alla.0004.0128 Aza.0198 .0016*.0386 .0672.0052* 0388.0064* .0170 0014 * Ama.0002,.0048, .0024.0002 .0002.0002 ula Per. - Int. .0628* - .0934 * Sala.1114* .1504* .1866*.1886* .1692 * .1290.1278 * .0942* 0960* .0780*.0778* .0534*.0526* 0 Per. - Per.Ord. .0012.0634* .0054.0932* .1110*.0128 .1484*.0270 Descriptions of Samples .0514 .0464.1716* .0224 .0088 .0036 .0006 Means of Means Interval50.008 49.940OrdinalSample A Percentile 49.563 Interval50.007 OrdinalSample49.947 B Percentile 49.594 MeanSD of SDsMeansSDs 1.8141.2303.416 1.7950.9983.463 24.94112.893 6.964 1.1293.7201.030 0.8043.7591.015 27.589 3.5137.334 Mean of Skews , 0.005 0.000 0.004 -0.990 -0.626 0.3820.009 MeanSDSD of of Skews Kurtosis -0.995 0.5050.617 -1.074 0.6160.595 -1.108 0.5260.595 0.5320.6001.739 -0.378 0.4851.174 -1.072 0.426 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR Normal (N = 5 ) andNegative Skewed(NTABLE =15 B) - 51 DISTRIBUTIONS :. Sales B .0010 .0050 .0100 .0250 Levels of Significance .0500 .0500 .0250 .0100 .0050 .0010 Int. - Ord.Int. .0030.0058 .0085.0164 .0176.0250 .0332.0480* .0598.0762* .0460.0420 .0222.0196 .0082 .0070 .0040.0036 .0006 Ord.Int. - -Int. Per. .0064.0000 .0186.Q302 .0298*.0008 .0526*.0042* .0826*.0112* .0410.0142* .0202.0048* .0008.0088 .0042.0002 .0004.0000 Ord. - Per.Ord. .0000.0036 .0002.0098 .0008.0200 .0042*.0372 .0112*.0656 .0128*.0454 .0048*.0232 .0006.0094 .0002.0046 .0000.004 Per. - Int.Ord. .0292*.0308* .0512*.0532* .0668*.0742* .1054*.1114* .1480*.1556* .1330*.1300* .0916*.0942* .0644*.0612* .0472*.0456* .0248*.0250* Per. - Per. .0008 .0060 Sample A .0102 .0278 Descriptions of Samples .0504 .0506 .0254 Sample B .0120 .0064 .0004 SDMeans of Meansof Means Interval50.019 1.822 49.950Ordinal 1.802 Percentile 49.876 4.315 Interval50.006 1.048 Ordinal49.942 1.031 Percentile 49.846 2.482 MeanSD of ofSDs SkewsSDs 0.0011.2403.392 -0.003 1.0113.445 -0.001 2.3408.265 -0.971 1.1123.697 -0.612 0.7913.746 '1.0121.1669.190 SDMean of ofKurtosisSkews Kurtosis -1.005 0.5030.610 -1.078 0.6590.592 -1.118 0.5180.585 0.4740.6001.706 -0.410 1.1620.489 -1.068 0.4290.387 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE Normal (N = 5) andNegative Skewed(N =15 ) TABL.L. B - 52 DISTRIBUTIONS FOR Int. - Int. A Scales B .0014.0010 .0050 .0068.0100 .0146.0250 Levels of Significance .0500 .0012*.0500 .0004*.0250 .0000.0100 .0000.0050 .0000.0010 Int.Int. - Ord.- Per. .0006.0014 AafiaADLA.0010 .0020.0086 .0048*.0192 ,012eAwe.0179 .0026*.0010* DDA,.0004* .0002.000Q .0000.0002 Ago..0000 Ord. - Int.Ord. .0016.0014 .0Q46.0054 .0062.0082. .0204.0154 .0382.0264* .0010* .0004*.0004* .0000 .0000 .0000.0000 to Per.Ord. - Int.Per. .0006 .0330*.0008 .0472*.0020 .0746*.0048* .1094!.0116* .0784*.0026* .0462.0008* * .0224*.0002 .0002.0128 .0000.0042 L.NI 1 Per.Per. - Ord.- Per. Alfa.0020.0212* .0432*.0062 .0134.0628* .0364.0994* .1390*.069Q .0276*.0856* .0554.0118 * .0016.0294* .0182.0016 .0004.0070 :,., Sample A Descriptions of Samples Sample B .., I ,) Interval Ordinal Percentile Interval 49.994 Ordinal51.162 Percentile 52.574 MeanMeansSD of of MeansSDs Means 49.983 1.7913.339 49.921 1.7913.417 24.65712.85349.429 18.4615.141 15.332 4.163 28.9907.732 MeanSD of SDsSkews 0.6120.0151.218 0.6000.0130.999 0.5970.0186.972 -0.990 0.6075.561 -0.801 0.5023.432 -0.041 0.3793.635 SDMean cf ofKurtosis Kurtosis -1.001 0.501 -1.066 0.693 -1.106 0.526 , 0.5121.776 0.0221.252 -1.102 0.419 TABU. B 53 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR Normal (N = 5 ) andNegative Skewed(N =15 ) DISTRIBUTIONS A Scales B .0010 .0050 .0088.0100 .0214.0250 Levels of Significance .0414.0500 .0036*.0500 .0010*.0250 .0000.0100 .0000.0050 .0000.0010 Int.Int. - -Int. Ord.Per. .0002.0026.0022 .0054.0052.0008 .0022.0090 .0046*.0204 .0094*.0426 .0;10*.0036* .0042*.0010* .0008.0000 .0002.0000 .0000 Ord. - Int. .0024 .0054.0056 .0092.0104 .0238.0232 .0434.0446 .0042*.0036* .0008*.0006* .0000.0000 .0000 .0000.0000 Ord. - Per.Ord. .0118.0002 .0262*.0012 .0022.0404* .0640*.0044* .0958*.0094* .0570.0100* .0322.0038* .0142.0002 .0074.0000 .0014.0000 Per. - Per.Ord.Int. .0018.0106 .0072.0266* .0120.0388* .0276.0634* .0974*.0536 .0444.0570 .0216.0300 .0082.0148 .0074.0052 .0010.0014 Sample A Descriptions of Samples Sample B t)r . Percentile SDMeans of Meansof Means Interval50.015 1.807 49.943Ordinal 1.794 Percentile 49.867 4.297 Interval50.012 2.051 Ordinall,50.097;2.014 50.039 2.446 MeanSD of ofSDs SkewsSDs 0.0221.2393.401 0.0171.0123.457 0.0232.3468.296 -1.000 2.2337.401 -0.960 2.0567.312 -0.017 1.1839.163 MeanSD of KurtosisSkews -1.002 0.6120.506 -1.068 0.6950.595 -1.112 0.5200.589 0.6001.743 0.5981.720 -1.047 0.3760.423 TABU . B - 54 OBTAINED PERCENTAGES OF t VALUES I'OR GIVEN LEVELS OF Normal (N = 15) andNaRative Skewed(N = 5 ) DISTRIBUTIONS Levels of Significance SIGNIFICANCE FOR Int. - Int. A Scales . B .0980*.0010 .1436*.0050 .1676*.0100 .2114*.0250 .2534*.0500 .1210*.0500 .0788*.0250 .0474*.0100 .0316*.0050 .0136.0010 Int. - Ord. .1004* .1168*.1534* .1378*.1834* .1846*.2336* .2304*.2762* .0942*.1334* .1028*.0626* .0740*.0392* .0600*.0264* .0378*.0124 Ord.Int. - -Int. Per. ,0916*_ono .1444* .1836*.1682* .2342*.2130 * .2776*.2554* .0924*.1204* .0612*.0764* .0368*.0466* .0306*.0256* .C132.0230 Ord.Ord. - -Ord. Per. .0810*.1030* .1174*.1534* .1384* .0112.1854* .0286*.2328* .0234*.1332* ,.1022* .0102 .0028.0736* .0014.0594* .0000.0332* 1 Per. - Int.Ord. .0004..0004 .0014.0018 .0034.0042 ,0098 ;J266* .0122* .0052* .0014 .0000 Per. - Per. .0036 .0116 Sample A .0178 .0470* Descriptions of Samples .0830* .0376 .0190 Sample B .0058 .0032 .0006 4.1 SDMeans of Meansof Means Interval49.989 1.040 49.934Ordinal 1.039 Percentile 49.516 7.473 Interval49.867 8.892 Ordinal51.202 7.254 Percentile 13.36052.753 MeanSD of ofSDs SkewsSDs -0.016 0.7203.798 -0.008 0.5183.821 27.528 0.0013.564 -0.44016.209 8.435 -0.37313.488 5.771 -0.02226.235 7.225 SDMean of ofKurtosisSkews Kurtosis -0.380 0.7880.520 -0.961 0.3740.494 -1.036 0.3870.448 -0.920 0.5960.578 -0.9590.5930.566 - 1.12'. 0.5230.593 TABLE 11 - 55 - OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF Normal (N =15 ) andNeaative Skewed(N = 5 SIGNIFICANCE) FORDISTRIBUTIONS Int. - Int. A Scales B .0156.0010 .0406*.0050 .0624*.0100 -.0250.1022* Levels of Significance .1462*.0500 .0864*.0500 .0472*.0250 .0224.0100 .0130.0050 .0028.0010 Int. - Ord.Per. .0250*.0210* .0490*.0454* .0652*.0658* .0968*.1030* .1312*.1446* .1294*.0840* .0910*.0476* .0240.0598* .0404*.0132 .0208*.0038 Ord. - Int. .0136 .0458*.0392* .0680*.0630* .10441.1036* .1492*.1476* .0802*.0800* .0462*.0444* .0226.0218 .0130.0122 .0030.0024 Ord.Ord. - -Ord. Per. .0244*.0194 .0504* .0034.0664* .0998*.0132 .0334.1324* .1264*.0242* .0106.0898* .0542*.0038 .0404*.0020 .0006.019k w t Per. - Ord.Int. .0000.0002 .0016.0018 .0040 .0140 .0352 .0222* .0102 .0034 .0016 .0006 0 Per. - Per. .0008 .0034 Sample A .0104 .0254 Descriptions of Samples .0510 .0392 .0172 Sample B .0058 .0028 .0010 SDMeans of Meansof Means Interval49.993 1.021 Ordinal49.929 1.019 Percentile 49.830 2.442 Interval 49.943 3.582 Ordinal50.018 3.522 Percentile 50.022 4.241 MeanMeanSD of ofSDs Skews -0.008 0.7283.807 -0.001 0.5213.831 0.0109.1911.190 -0,438 6.4873.379 -0.528 6.4493.161 0.0022.3098.316 MeanSD of KurtosisSkews -0.368 0.7780.532 -0.964 0.4680.375 -1.041 0.4270.389 -0.922 0.5820.596 -1.553 0.5651.166 -1.108 0.5160.589 TALLF B 56 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN Normal (N Q 5 ) and Leptokurtic LEVELS OF SIGNIFICANCE = 5 ) DISTRIBUTIONS FOR Int. - Int. A Scales B .0004.0010 .0026.0050 .0068.0100 .0186.0250 Levels of Significance .0420.0500 .0462.0500 .0268.0250 .0112.0100 .0050.0056 .0010.0016 Int. - Per.Ord. .0124.0004 .0034.0230. .0302*.0076 .0444*.0222 .0634.0449, .0672.0526 03272.0487* ..0132-91312# .0250*.0070 .0158.0014 Ord. - Int.Ord. .0012 .0052.0046 .0088.0088 .0218.0230 .0450.0456 .0496.0454 .0280.0256 .0124.0114 ,0076ADZ, .0014Dla to Per.Ord. - Int.Per. .0096.0124 .0198.0232 .0280.0300* .0474*.0446* .0704*.0638 .0664.0662 .0412.0480* .0270.0312* .0198.0256* .0112.0155 a,Lit t Per. - Per.Ord. .0090.0014 .0200.0066 .0110.0278 .0258.0464* .0498.0704* .0506.0670 .0276.0416 .0272.0136 .0194.0086 .0022.0110 Interval OrdinalSample A Percentile Descriptions of Samples Interval OrdinalSample B Percentile 49.926 MeanSDMeans of ofMeansof SDs Means 50.043 3.3981.798 49.971 3.4561.786 24.89312.84249.783 50.038 2.1763.712 49.979 3.9372.123 27.76714.029 MeanSD of ofSDs Skews 0.0081.243 0.0031.010 0.0046.991 -0.004 2.432 -0.007 0.6761.876 0.6420.0027.194 SDMean of ofKurtosisSkews Kurtosis -1.005 0.4960.610 -1.086 0.5940.560 -1.117 0.5170.589 -0.906 0.6580.764 -1.035 1.772 -1.148 0.581 OBTAINED PERCENTAGES OF t VALUES FOR .IVEN LEVELS TABLE B 57 OF SIGNIFICANCE FOR Scales B .0010 .0050Normal .0100 (N = 5 0250) and Leptokurtic Levels of Significance .0500 .0500 (N = 5 ) DISTRIBUTIONS .0250 .0100 .0050 .0010 Int. - Int. A .0012 .0048 .0120.0094 .0244.0260 .0454.0462 .0434.0492 .0240.0208 .0080.0070 .0046.0036 .0014.0010 Ord.Int. - -Int. Ord.Per. .0014.0070.0018 .0056.0070.0146 .0128.0202 .0280.0346 .0502.0534 .0426.0602 .0408.0220 .0092.0250 .0160.0038 .0010.0104 Ord. - Ord. .0014 .0070 .0124 .0280 .0478 . .0468 .0242 .0088 .0044 .0014 Per.Ord. - Int.Per. .0064.0068 .0152.0158 .0242.0212 .0350.0396 .0534.0644 .0602.0588 .0334.0388 .0234.0166 .0122.0152 .0060.0042 t.n Per. - Per.Ord. .0022.0052 .0076.0142 -----.0140.0218 .0278.0376 .0486.0630 .0472.0588 .0336.0268 .0104.0168 .0106.0060 .0022.0032 Interval OrdinalSample A Percentile Descriptions of Samples Interval49.984 OrdinalSample49.935 B Percentile 49.880 MeanMeansSD of of MeansSDs Means 50.010 3.4111.827 49.942 3.4571.818 49.880 4.3508.297 3.7062.130 2.0963.948 9.2884.595 MeanSD of ofSDs Skews -0.005 1.241 - 0.003 1.002 -0.001 2.330 -0.009 2.389 -0.005 1.872 0.0162.348 MeanSDSD of of Skews Kurtosis -0.997 0.6130.499 - 1.089 0.5570.593 -1.115 0.5190.588 -0.916 0.7580.656 -1.074 0.6651.558 -1.162 0.5790.629 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR TABLL - 58 A Scales B .0010 .0050Normal .0100 (N 5 .0250 ) and Leptokurtic Levels of Significance .0500 .0500 (N = 5 ) DISTRIBUTIONS .0250 .0100 .0050 .0010 Int.Int. - -Int. Ord. .0068.0054 .0166.0110 .0226.0166 .0368.0306 .0554.0520 ,0616 .,0314.0384 .0250.0202 .0196.0156 .0112.0088 Ord.Int. - -Int. Per. .0070.0050 .0108.0190 .0274.0158 .0308.0450* .0508.0662 ,0734* .0330.0548* .0206.0314* .0154.0228 .0084.0136 Ord.Ord. - -Ord. Per. .0070.0068 .0190.0164 .0220.0276 .0454*.0376 .0672.0544 .0604,0546.0734* .0540*.0286 .0312*.0244 .0232.0190 .0128.0110 co Per. - Ord.Int. .0022.0026 .0088.0090 .0140.0154 .0312.0328 .0558.0536 .0538.0512 .0306.0334 .0192.0174 .0108.0096 .0036.0038 Per. - Per. .0016 .0066 Sample A .0100 .0240 Descriptions of Samples .0476 .0534 .0304 Sample B .0154 .0090 .0030 MeansSD of of Means Means Interval49.981 1.786 49.918Ordinal 1.782 Percentile 49.40212.871 Interval49.90210.828 49.700Ordinal 7.988 Percentile 49.58315.334 MeanSD of ofSDs SDsSkews 14.3510.0021.223 0.0011.0143.424 24.677 0.0097.085 -0.00211.86318.675 -0.00415.106 5.613 29.820 0.0127.652 MeanSDSD of of Skews Kurtosis -0.999 0.6130.500 -1.069 0.5810.599 -1.105 0.5180.592 -0.909 0.6120.761 -1.038 0.5810.674 -1.146 0.5630.627 TABLE B - 59 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE Normal (N 5 ) and Leptokurtic (N 5 ) DISTRIBUTIONS FOR Int. - Int. A Scales B .0024.0010 .0078.0050 .0132.0100 .0250.0248 Levels of Significance .0500.0510 .0500.0500 .0250.0244 .0100.0140 .0050.0086 .0010.0028 Int. - Per.Ord. .0054.0044 .0098.0142 .0186.0146 .0286.0364 .0600.0518 .0632.0504 .0362.0256 .0212.0156 .0128.0102 .0058.0038 Ord. - Int.Ord. .0034.0014 .0094.0076 .0134.0122 .0298.0256 .0538.0512 .0468.0458 .0260.0244 .0158.0132 .0094.0080 .0032.0020 oa Ord. - Per. .0048 .0134 .0198.0136 .0304.0366 .0576.0616 .0500.0606 .0252.0354 .0130.0208 .0060.0130 .0014.0050 VD43, Per. - Int.Ord. .0020.0012 .0072 .0156 .0310 .0582 .0492 .0276 .0124 .0062 .0016 Per. - Per. .0018 .0070 Sample A .0138 .0288 Descriptions of Samples .0548 .0498 .0268 Sample B .0134 .0080 .0016 MeansSD of of Means Means Interval 49.988 1.772 Ordinal49.920 1.778 Percentile 49.804 4.254 Interval49.920 4.422 49.995Ordinal3.620 Percentile 49.878 4.262 MeanMeanSD of ofSDs Skews 0.0221.2063.355 0.0180.9883.427 0.0182.3128.244 4.8030.0157.478 0.0186.4723.381 0.0132.2888.303 SDMean of ofSkewsKurtosis Kurtosis -1.0070.6070.502 -1.061 0.9350.592 -1.117 0.5180.585 -0.919 0.7420.603 -0.979 0.7601.503 -1.108 0.5240.594 TABLE B - 60 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF Normal (N = 15) and Leptokurtic (N 15) SIGNIFICANCE DISTRIBUTIONS FOR Int. - Int. A Scales B .0006.0010 .0034.0050 .0080..0100 .0218.0250 Levels of Significance _D47g.0500 .0522.0500 .0260.0250 .0100.0092 .0050 .0010,.0010 Int. - Ord.Per. .0032.0006 .0088.0040 .0086 .0284.0226 .0506_044A .0628.0544 ,aak.0352 .0178.0128 AI164.0130 .0014.0056 Ord.Ord. - -Ord. Int. .0008.0006 .0050.0042 A150.0096.0086 .0246.0250 .0528.0490 .0484.0470 .0270.0230 .0088.0116 .0062.0052 .0012.0014 Per.Ord. - Int.Per. .0032 .0090 .0150.0142 .0284.0298 .0566.0510 .0458.0626 .0248.0354 .0144.0180 .0132.0102 .0042.0056 0cr. Per. - Per.Ord. .0012.0032 .0070.0084 .0114.0138 .02920252 .0518.0558 .0460.0496 .0250.0282 .0126.0144 .0078.0102 :0022.0042 Interval OrdinalSample A Percentile Descriptions of Samples Interval 49.943OrdinalSample B Percentile 49.649 MeanSDMeans of of Meansof SDs Means 50.000 1.0333.821 49.936 1.0293.840 49.54027.6107.399 49.996 1.;2.844.365 4.467 1.264 30.563 8.265 MeanSD of SDsSkews 0.0020.726 -0.002 0.517 0.0093.533 0.0021.8571.215 0.8390.0021.379 0.0170.4223.371 SDMean of ofKurtosisSkews Kurtosis -0.369 0.7680.516 -0.967 0.3700.467 -1.044 0.3830.431 2.3021.114 -0.133 1.743 -1.253 0.431 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN TABLE u - 61 LEVELS OF SIGNIFICANCE FOR A Scales B .0010 .0050Normal .0100 (N = 19 and Leptokurtic .0250 Levels of Significance .0500 .0500 (N = 15) DISTRIBUTIONS .0250 .0100 .0050 .0010 Int. - Int.Ord. .0020 .0052 .0132.0116 _n24g ,/IFS.0458 .0560.0482 .0312.0230 ,0138.0092 .0078.0046 .0008.0024 Ord.Int. - -Int. Per. Ma.0020028 ,034.0052.Q068 .0116.0130 _Lam.0254.0288 .0476.0498 .0486.0576 .0222.0336 .0156.0090 .0048.0096 .0008.0030, Ord.Ord. - -Ord. Per. .0028.0026 .0066.0086 .0132.0136 .0288.0292 .0502.0484 .0568.0544 .0310.0334 .0160.0128 .0080.0096 .0030.0022 t.-_. .0010 .0044 .0102 .0254 .0534 .0484 .0230 .0080 .0046 .0010 cni-. 1 Per. - Ord.Int. .0010 .0056 .0124 .0282 .0560 .0462 .0236 .0106 .0064 .0018 Per. - Per. .0014 .0068 Sample A .0108 .0288 Descriptions of Samples .0524 .0458 .0236 Sample B .0096 .0050 .0014 SDMeans of Meansof Means Interval49.993 1.023 Ordinal49.926 1.027 Percentile 49.445 7.386 Interval49.986 6.455 49.826Ordinal 4.643 Percentile49.738 8.852 MeanSD of ofSDs SkewsSDs 0.0110.7153.779 0.5110.0083.818 27.481 0.0173.494 22.204 O.uuLc_483 17.0920.0043.563 33.104 0.0173.693 SDMean of ofKurtosisSkews Kurtosis -0.380 0.7820.526 -0.9640.3770.476 -1.040 0.3880.426 2.2911.0751.199 -0.421 0.6291.015 -1.236 0.4120.406 OBTAINED PERCENTAGES OF t ',7ALUES FOR GIVEN LEVELS OF SIGNIFICANCE TABLE B - 62 FOR Scales Normal (N = 5) and Leptokurtic Levels of Significance (N = 15) DISTRIBUTIONS Int. - Int. A B .0010.0010 .0048.0050 .0100.0100 .0202.0250 .0430.0500 .050001.,ill .0242.0250 .0112,.0100 .0058.0050 .0012.0010 Int. - Per.Ord. A000 .0000.0028 .0006.0060 .0018*.0148 .0056*.0348 .0436 .0026*.0206 .0082.0010 .0004.0036 .0000.0010 Ord.Ord. - -Ord. Int. .0020.DI01.0004 .0074.0040 .0070.0128 .0178.0248 .0400.0468 .0432.0486032, .0198.0260 .0092.0112 . .0070 .0044 .nni4.0010 to Per.Ord. - Int.Per. ,0000 .0834*.0000 .1046*.0006 .1408*.0020* .1786*.0054* .1742*.0080* .1364*.0028* .0012.0984* .0792*.0004 .0514*.0000 Cf,rs.) Per. - Ord. .0538*.046* .0822* .1044* .1416* .1790* .1752* .1364* .0996* .0800* .0506* Per. - Per. .0004 .0026 Sample A ma .0174 Descriptions of Samples .0384 .0422 .0214 Sample B .0070 .0032 .0014 MeansSD of of Means Means Interval50.018 1.761 49.955Ordinal1.761 Percentile 12.65749.672 Interval49.983 1.274 49.929Ordinal 1.248 Percentile 49.638 8.181 MeanSD of SDsSkews 0.0111.2193.353 0.0130.9913.425 24.6900.0136.925 -0.006 4.4121.905 -0.012 1.3904.500 30.668 0.0203.293 MeanSD of KurtosisSkews -1.000 0.4960.604 -1.076 0.5880.565 -1.110 0.5150.584 2.3261.1411.220 -0.112 1.7740.849 -1.256 0.4410.423 TABLE D - 63 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR Normal (N =5 ) and Le rokurtir (N m15 ) DISTRIBUTIONS Int. - Int. A Scales B .0010.0010 .0050 .0100.0102 .0250.0246 Levels of Significance .0488.0500 .0500.0502 .0272.0250 .0100.0102 .0046.0050 .0010 Int. - Per.Ord. .0000.0002 .0030.0004 .0006.0060 .0032*.0162 .0104*.0408 .0094*.0436 .0034*.0202 .0010.0080 .0006.0040 .0000.0006 Ord. - Ord.Int. .0012.0014 .0042.0070 .0078.0120 .0202.0288 .0440.0534 .0412.0500 .0212.0264 .0078.0102 .0060.0036 .0008.0010 Ord. - Per. .0246*.0000 .0480*.0004 .0644*.0008 .1022*.0036* .1420*.0108* .1210*.0082* .0030*.0918* .0576*.0012 .0414*.0006 .0206*.0000 Per.Per. - -Int. Ord. .0208* .0040.0418* .0076.0588* .0196.0982* .0446.1362* .0408.1216* .0188.0878* .0066.0552* .0386*.0028 .0004.0174 Per. - Per. .0006 Interval OrdinalSample A Percentile Descriptions of Samples Interval OrdinalSample B Percentile MeansSD of of Means Means 50.006 1.819 49.937 3.4431.809 49.851 8.2684.327 50.016 4.3481.248 49.961 4.4651.229 10.20349.927 2.713 MeanSD of SDsSkews - 0.002 1.2473.393 -0.004 1.009 0.0022.341 0.0161.811 0.0071.332 0.0101.095 SDMean of ofKurtosisSkews Kurtosis - 1.007 0.4970.606 -1.076 0.7250.594 -1.116 0.5170.588 2.2891.0981.205 -0.139 0.8311.729 -1.257 0.4210.419 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR TABLE B - 64 A Scales .0010 .0050 Normal .0100 (N = 5 ) and .0250 Levels of SignificanceLeptokurtic.0500 .0500 (N = 15) DISTRIBUTIONS .0250 .0100 .0050 .0010 Int.Int. - -Ord. Int. .0000.0000 .0002.0000 .0008.0006 .0022*.0018* .0062.0044. .0068*.0058* .0028*.0020* .0016.0008 .0006.0004 .0004.0002 Ord.Int. - -Int. Per. .0000 .0000 .0004 .0016*.0022* .0052*.0064* .0064*.0082 * .0042 * .0008.0012 .0008.0002 .0004.0002 Ord. - Per.Ord. .0000.0000 .0000.0002 .0004.0010 .0024*.0022 * .0066*0062 * .0078*.0066* ,L101/6!.0040* .0012.0016 .0008.0004 .0004 Per. - Int.Ord. .0098.0074 .0242*.0182 .0384*.0288 .0650.0508* * .1008*.0828* .0998*.0770* .0602.0464* * .0332*.0238 .0228.0166 .0086.0046 Per. - Per. .0006 .0032 Sample A .0066 .0152 Descriptions of Samples .0368 .0344 .0170 Sample B .0068 .0040 .0008 SDMeans of Meansof Means Interval50.024 1.774 49.960Ordinal 1.776 Percentile 49.70612.786 Interval49.848 6.548 49.802Ordinal4.669 Percentiles 49.724 8.972 MeanSD of ofSDs SkewsSDs 0.0111.2093.360 0.0090.9903.434 24.753 0.0096.915 -0.03322.238 9.506 -0.00117.065 3.475 33.1150.0263.681 SDMean of ofKurtosisSkews Kurtosis -0.997 0.5090.614 -1.068 0.6640.598 -1.104 0.5220.595 2.2511.0431.177 -0.425 0.6371.013 -1.239 0.4110.407 TABLE B - 65 OBTAINED PERCENTAGES OF t VALUES Normal (N 5 ) and Leptokurtic FOR GIVEN LEVELS OF SIGNIFICANCE (N =15 ) DISTRIBUTIONS FOR Int. - Int. A Scales B .0000.0010 .0004.0050 .0012.0100 .0044*.0250 Levels of Significance .0138*.0500 .0158*.0500 .0062.0250 .0024.0100 .0014.0050 .0010.0000 Int. - Per.Ord. .0002 .0004,.0008 .0008.0016 .0040*.0062 .0184*.0122* .0206*.0146* .0054*.0070 .0018.0022 .0012 .0000.0002 Ord.Ord. - -Ord. Int. 021.0000 .0004.0008 .0018.0014 .0062.0074 .0148*.0190* .0152*.0202* .0072.0060 .0026.0028 .0014 .0004 Per.Ord. - Int.Per. .0044.0002 .0004.0124 .0198.0008 .0042*.0412 .0126*.0688 .0144*.0632 .0380.0068 .0190.0020 .0010.0116 .0048.0000 o. Per. - Per.Ord. .0070.0004 .0052.0156 .0118.0258 .0284.0510* .0566.0798* .0560.0736* .0452*.0274 .0118.0252 .0070.0140 .0060.0012 Interval OrdinalSample A Percentile Descriptions of Samples Interval 49.948 OrdinalSample49.986 B Percentile 49.892 MeanSDMeans of of Meansof SDs Means 50.020 3.3751.820 49.953 1.8083.431 49.889 4.3358.236 8.8842.610 2.1217.450 9.2062.501 MeanSD of ofSDs Skews 0.0111.246 0.0091.015 0.0112.348 0.0251.1963.742 0.9920.0282.374 0.3940.0211.185 MeanSD of KurtosisSkews -0.995 0.6150.502 -1.0790.5990.5148 -1.1090.5940.)23 2.3091.045 1.9300.324 -1.058 0.454 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR TABLE A Scales B .0010 .0050 Normal .0100 (N = 13 and.0250 Leptokurtic Levels of Significance .0500 .0500 (N = 5) .0250 DISTRIBUTIONS .0100 .0050 .0010 Int. - Ord.Int. .0354*.0382* .0660*.0626* .0848*.086R* .1306*.1260* .1654*.1790* .1720*.1762* _1202'.1300* .0846*.0934* .0708*.0628* .0428*.0154* Ord.Int. - -Int. Per. .0356*.0576* .0632*.0830* ...0258,.1016* ...lane.1324* .1802*.1794* .1814*.1742* .1282*.1434* .0842*.1064* .0892*.0624* .0344*.0620* Ord. - Per.Ord. .0378.0586* * .0828*.0674 * .1020*.0874* .1368*.1272* .1800*.1680* .1812.1706* * .1436*.1298* .0914*.1064* .0880*.0706* .0620*.0422* CAam Per. - Ord.Int. .0000 .0008.0014 .0022.0040 .0084.0140 .0218*.0318 .0230*.0296 .0086.0102 .0020.0024 .0010 .0006.0004 Per. - Per. .0026 .0106 Sample A .0178 .0426 Descriptions of Samples .0762* .0732* .0406 Sample B .0196 L0104 .0024 MeansSD of of Means Means Interval49.998 1.035 49.931Ordinal 1.030 Percentile 49.498 7.423 Interval50.03710.813 49.830Ordinal 7.955 Percentile15.28849.825 MeanSD of ofSDs SkewsSDs 0.0030.7383.821 0.0050.5283.838 27.6140.0133.615 11.87918.479 0.006 -0.0J015.126 5.553 29.908 0.0027.731 MeanSD of KurtosisSkews -0.369 0.8090.526 -0.959 0.4950.379 -1.042 0.4380.385 -0.9280.6120.750 -1.054 0.5820.666 -1.152 0.5690.629 TABLE B - 67 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR Normal (N =15 ) and Leptokurtic (N * 5 ) DISTRIBUTIONS A Scales B .0010 .0282*.0050 .0450*.0100 .0832*.0250 Levels of Significance .1262*.0500 .0500.1150* .0250.0720* .0100.0386* .0236.0050 .0080.0010 Int. - Ord.Int.Per. .0266*.0090.0086 .0532*.0268* .0702*.0430* .1010*.0780* .1410*.1166* .1362*.0990* .0620*.1004* .0624*.0346* .0480*.0202 .0230*.0070 Ord. - Int.Ord. .0076.0080 .0266*.0278* .0416*.0448* .0784*.0820* .1206*.1268* .0996*.1134* .0598*.0698* .0312*.0350* .0200.0226 .0058.0066 Per.Ord. - Int.Per. .0262*.0006 .0040.0538* .0080.0708* .0230.1012* .0468.1416* .1332*.0356 .0132.0090* .0046.0610* .0026.0456* .0232*.0004 -..,cAw 1 Per. - Ord. .0004 .0038 .0070 .0182 .0374 .0274* .0094 .0034 .0014 .0002 Per. - Per. .0014 .0060 Sample A .0116 .0300 Descriptions of Samples .0554 .0494 .0220 Sample B .0076 .0038 .0010 MeansSD of of Means Means Interval49.991 1.042 49.928Ordinal 1.038 Percentile 49.827 2.487 Interval50.029 4.455 50.060Ordinal 3.705 Percentile 49.974 4.346 MeanSD of SDsSkews 0.0010.7363.820 0.0040.5263.834 0.0129.1961.200 0.0084.6667.457 0.0063.3456.489 0.0038.2732.297 SDMean of ofKurtosisSkews Kurtosis -0.365 0.7880.528 -0.960 0.3750.478 -1.040 0.3860.434 -0.913 0.6110.755 -0.361 0.7740.861 -1.112 0.5960.526 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR TABLE. B - 68 A Scales B .0010 positive Skewed .0050 .0100 (N = 5 .0250 ) and Positive SkemeAN = 5 Levels of Significance .0500 .0500 ) DISTRIBUTIONS.0250 .0100 .0050 .0010 Int. - Ord.Int. .0014.0010 .0050.0040 .0114.0072 .0240.0186 .0500.0408 _0422 nist, .0172 -0068.0064 .0030.0026 .0006 Ord.Int. - -Int. Per. -008. .0040.0194 .0076.0270 .0160.0444* .0396.0718* _05n4 nro, _awl.0248nAan* .0294* .0214 .0102.0008 Ord.Ord. - -Ord. Per. A010.0086.0014 .0188.0046 .0262.0096 .0438.0204 .0442.0722* .0672.0470 .0448*.0216 ,0088Ami..0298* 046 .0216.0038 .0010.0098 Per.Per. - -Ord. Int. .0096.0098 .0212.0214 .0282.0284 .0442.0448* * .0656.0642 ....Dfdi.0Q68 .0102,.0448* .0284.0280 .0212.0224 .0100 Per. - Per. .0018 .0054 Sample A .0116 .0232 Descriptions of Samples .0438 ,0480 .0250 Sample B .0098 .0050 .0014 MeansSD of of Means Means Interval 50.010 1.785 Ordinal50.037 1.767 Percentile 50.26712.706 Interval49.998 1.812 50.027Ordinal1.794 Percentile 50.13912.852 MeanMeanSD of ofSDs Skews 0.4401.6523.217 0.3161.2933.356 24.873 0.0066.883 0.4301.6733.203 0.3121.3093.347 24.875 0.0016.916 SDMean of ofKurtosisSkews Kurtosis -0.907 0.5920.604 -0.984 1.3280.602 -1.117 0.5210.589 -0.920 0.5930.601 -0.997 1.2260.604 -1.118 0.5230.592 TABLE B - 69 OBTAINED PERCENTAGES OF t VALUESPositive FOR GIVEN Skewed LEVELS OF SIGNIFICANCE (N . 5 ) andPositive Skewed(N 5 ) DISTRIBUTIONS FOR Int. - Int. A Scales B .0012.0010 .0032.0050 .0072.0100 .0250.0212 Levels of Significance .0500.0470 .05000426 .0196.0250 .0068.0100 .0034.0050 .0010.0008 Int.Int. - -Per. Ord. .0068.0018 .0152.0050 .0244.0102 .0438.0294 .0688.0564 .0562.0390 .0346.0196 .0198.0060 .0126.0028 .0030.0004 Ord.Ord. - -Ord. Int. .0016.0006 .0032.0048 .0086.0074 .0196.0254 .0494.0430 .0474.0522 .0216.0240 .0124.0106 .0044.0066 .0014.0016 to Per.Ord. - Int.Per. .0040.0052 .0116.0142 .0180.0224 .0320.0412 .0618.0674 .0576.0680 .0420.0360 .0252.0200 .0164.0132 .0068.0026 q)cs. 1 Per. - Ord.Per. .0018.0034 .0062.0112 .0104.0180 .0268.0344 .0624.0542 .0460.0634 .0268.0394 .0132.0232 .0072.0152 .0022.0054 .fa. V Interval OrdinalSample A Percentile Descriptions of Samples Interval OrdinalSample B Percentile MeanSDMeans of ofMeansof SDsMeans 49.997 3.2021.789 50.030 3.3471.782 50.068 4.302 50.036 1.7973.238 50.067 1.7823.369 50.145 4.2838.335 MeanSD of ofSDs Skews 0.4441.643 0.3311.288 0.0182.298 0.4351.672 0.3121.313 -0.000 0.5912.321 MeanSDSD of of Skews Kurtosis -0.910 0.5990.603 -1.000 0.6040.838 -1.114 0.5940.528 -0.926 0.5980.595 -1.004 1.3610.599 -1.119 0.524 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN TABLL B 70 LEVELS OF SIGNIFICANCE FOR Scales .0010 Positive Skewed .0050 .0100 (N = 5) and Positive Skewed(N = 5) .0250 Levels of Significance .0500 .0500 .0250DISTRIBUTIONS .0100 .0050 .0010 Int. - Int.Ord. A B .0006.0004 .0032.0028 .0058.0054 .0114.0106 .0198*.0236* 1427*1SAA* .1158*wl* .0804*.0708* .0590*.0478* .0272*.0246* Ord.Int. - Int.Per. .0002. 080 Aug.0022 .0046.0196 .0108.0312 .0236*.0446 .1008*.1420* .0690*.1030* .0432*.0708* .0324*.0482* .0242*.0152 Ord.Ord. - -Ord. Per. .0074.0004 .0140.0028 .0048.0194 ,0314Ala .0450.0200* .1012*.1570* .1176*'.0696* .0796*.0434* .0586*.0328* .0268*.0152 - I Per. - Int. .0022 .0068 .0114 .0232 .0492 .0646 .0388 .0254 .0144 .0068 c,-..., Per. - Ord.Per. .0026.0018 .0048.0076 .0096.0124 .0236.0192 .0390.0474 .0714*.0728* .0392.0440* .0284.0194 .0166.0096 .0066.0030 Interval OrdinalSample A Percentile Descriptions of Samples Interval OrdinalSample B Percentile 46.405 MeanSDMeans of of Meansof SDs Means 49.951 3.1461.789 49.984 3.3031.792 24.72712.99549.944 15.87250.023 8.898 13.53048.401 7.322 26.21013.574 MeanSD of ofSDs Skews 0.4341.612 0.3181.274 0.0096.930 0.4288.265 0.6020.3675.782 0.5970.0357.244 MeanSDSD of of Skews Kurtosis -0.917 0.5850.599 -0.992 0.6041.148 -1.117 0.5230.590 -0.927 0.5780.598 -0.953 0.567 -1.120 0.526 TABLE B - 71 OBTAINED PERCENTAGES OF t VALUES FOR Positive Skewed (N mg 5 ) andPositive GIVEN LEVELS OF SIGNIFICANCE FOR Skewed(N =5 ) DISTRIBUTIONS A Scales B .0010 .0050 .0100 .0250 Levels of Significance .0500 .0500 - .0250 .0100 .0050 .0010 Int. - Int. .0016.0006 .0032 .0078.0060 .0154,.0124 ,0294*.0366 ,0288*.1048* .0636*.0644* .0306*.0372* .024Z.0172 .0038.0090 Ord.Int. - Int.Per.Ord. .0004.0074 .0059.0032.0184 .0052.0286 .0114.0470* .0264*.0766* .1086*.0566 .0676*.0326 .0320*Djaz ,0168 .0108 .0042.0040 Ord.Ord. - Ord. - Per. .0062.0016 .0162.0046 .0068.0276 .0448*.0134 .0714*.0318 .0410.1010* .0340.0664* .0180.0364* .0114.0226 .0036.0074 -4 Per. - Int.Ord. .0016.0004 .0048 .0076.0080 .0190.0168 .0390.0374 .0698*.0746* .0420.0436 .0206.0232 .0128.0144 .0038.0036 Per. - Per. .0030 .0074 Sample A .0124 .0254 Descriptions of Samples .0554 .0546 .0282 Sample B .0108 Percentile .0062 .0012 MeansSD of of Means Means Interval50.009 1.791 50.044Ordinal 1.794 Percentile 50.111 4.326 Interval50.109 3.660 50.232Ordinal 3.665 50.301 4.327 MeanSD of ofSDs SkewsSDs 0.4271.6223.192 0.3021.2733.338 -0.006 2.2858.295 0.4366.4073.317 0.5176.4893.199 -0.017 2.3318.248 MeanSD of SkewsKurtosis -0.925 0.5900.595 -1.018 0.9520.602 -1.120 0.5230.590 -0.914 0.5780.602 -1.285 1.1480.880 -1.098 0.597 .521 OBTAINED PERCENTAGES OF t VALUESPositive FOR Skewed GIVEN (N = 5 ) andPositive Skewed(N = 5 TABLE B 72 LEVELS OF SIGNIFICANCE FOR ) DISTRIBUTIONS Int. - Int. A Scales B .0002.0010 .0024.0050 .0042.0100 .0122.0250 Levels of Significance A0238*.0500 .0920*.0500 .0558*.0250 .0100 0312* .0050 .0046.0010 Int. - Ord.Per. .0012.0034 .0132 Aga.0236 .0408.0136 .0298*.0718* .0884*0384 .0588*.0190 ..0366* ,susA.0038.0256* .0104.0010 Ord.Ord. - -Ord. Int. -0002.0004 .0030.0018Ma .0032.0056 0106.0126 .0284!'.0220* A824,.0944* .0584*.0588* WA.0388*.0322* .0240.0194 .0094.0062 Per.Ord. - Int.Per. .0024.0002 .0088.0008 .0186.0032 .0084.0364 .0224*.0622 .0922*.0408 .0564*.0216 .0326*.0094 .0048.0192 .0074.0014 Per. - Per.Ord. .0016.0002 .0056.0024 .0128.0034 .0262.0116 .0276*.0544 .0484.0820* .0276.0530* .0128.0308* .0088.0218 .0024.0088 Interval OrdinalSample A Percentile Descriptions of Samples Interval50.080 50.216OrdinalSample B Percentile 50.144 MeansMeanSD of ofof Means MeansSDs 50.021 1.8083.166 50.064 1.8083.321 50.085 4.1142.175 6.4303.556 6.5263.592 4.1342.113 MeanSD of ofSDs Skews 0.4191.642 0.3031.300 -0.005 1.170 0.5980.4423.296 0.6220.5053.185 -0.016 0.5891.148 MeanSD of KurtosisSkews -0.925 0.6090.603 -0.992 0.6141.218 -1.112 0.5980.531 -0.912 0.574 -2.054 .781 -1.107 0.523 TABLE B - 73 OBTAINED PERCENTAGES OFPositive t VALUES Skewed FOR (N =15 ) andPositive Skewed(N = GIVEN LEVELS OF SIGNIFICANCE FOR 15) DISTRIBUTIONS A Scales B .0010 .0050 .0100 .0232.0250 Levels of Significance .0500.0438 .0500 .0260.0250 .0112.0100 .0056.0050 .0010 Int. - Ord.Int. .0010.0004 .0052.0036 .0108.0074 .0282 051fi _DARE.0522.0428 0232.0290 .0148.0086 .0096.0056 AMA.0042.0014 Ord.Int. - -Int. Per. .0018.0004 .0028.0076 .0052 0126 .0184.0310 X0558.0390 .0600 .0318 .0124.0150 .0068.0080 .0020.0026 Ord.Ord. - -Ord. Per. .0020.0010 .0074.0034 .0120.0084 .0312.0238 .0546.0464 .0642.0536.0518 .0356.0300.0278 .0176.0148 AW.0120 042. Per. - Ord.Int. .0036 .0086 .0138.0136 .0280.0272 _.0490.0494 .0536.0642 .0276.0346 .0142.0172 .0088.0124 .0026.0034022. Per. - Per. .0012 Interval .0032 OrdinalSample A .0096 Percentile.0244 Descriptions of Samples .0496 Interval OrdinalSample B Percentile MeanMeansSD of of MeansSDs Means 50.022 1.0473.724 50.057 3.7941.042 27.67750.372 7.510 50.007 3.7381.045 50.040 3.8021.040 27.69550.202 7.432 MeanSD of ofSDs Skews 1.1230.971 0.8110.607 0.0003.526 0.6140.9901.145 0.4960.6200.826 0.3850.0063.509 MeanSD of KurtosisSkews 1.7050.4760.600 -0.420 1.1420.487 -1.067 0.4170.386 1.7540.540 -0.385 1.199 -1.070 0.432 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR TABLE B 74 A Scales B .0010 Positive Skewed .0050 .0100 (N =15 ) and Positive Skewed(N = 15) .0250 Levels of Significance .0500 .0500 .0250 DISTRIBUTIONS .0100 .0050 .0010 Int. - Int.Ord. ALIO.00911 .0004.0006 .0018.0024 A0E8 .0118*.0230* .1500*.1070* ,DIZA,.0708* .0620*.0442* ,0442*.0338* .0150.0210* Ord.Int. - -Int. Per. -ELM.0000 .0006.0026 ma.0024 ADO,.0062.0098 .0222*.0180* ,1184*.1074* .0722*.0694* .0450*.0352* .0338*.0218 .0064.0158 Ord. - Per.Ord. .0006.11024 .0026.0006 .0036.0016 .0100.0042* .0178*.0114* .1508*.1196* .0692*.1008* .0350*.0636* .0218.0450* .0068.0216* Per.Per. - -Ord. Int. ,0006.0006 .0024 .0050.0068 .0138.0188 .0278*.0388 .0792*.0582 .0434.0294 .0236.0176 ,0104.0136 .0046.0036 Per. - Per. .0002 .0016 Sample A .0030 .0094 Descriptions of Samples .0222* .0950* .0520* Sample B .0258 .0124 .0034 SDMeans of Meansof Means Interval49.993 1.031 50.033Ordinal 1.031 Percentile 50.228 7.453 Interval50.005 5.140 .48.390Ordinal 4.219 Percentile 46.317 7.777 MeanSDMean of ofSDsSkews SDs 0.9711.1203.700 0.6090.8083.780 27.6500.0013.496 18.515 0.9865.690 15.552 0.8073.521 29.2420.0703.659 SDMean of ofKurtosisSkews Kurtosis 1.7360.4920.607 -0.410 1.1780.490 -1.065 0.4320.385 1.7350.5040.604 1.2530.0490.505 -1.090 0.4170.383 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN TABLE B 75 LEVELS OF SIGNIFICANCE FOR Scales Positive Skewed (N = 15) andPositive Skewed(N .0100 .0250 Levels of Significance .0500 .0500 =15 ) DISTRIBUTIONS.0250 .0100 .0050 .0010 Int. - Ord.Int. A B .0000.0010 .0018.0050 ,0011.0050 al210 .0404.0338 .0768*.0848* .0420.050 .0202.0262 .0140.0144 .004Q.0044 Ord.Int. - Int.Per. .0000.0036 Aga.0012.0110 01232.0182 .01400261A20 .0306.0652 .0884*.9422 .0534*.0214 A282....026 .0156.0052 .0060.0018 Ord. - Ord. .0000. .0098.0016 .0042.0172 .0156.0352, .0640.0370 .0448.0802* .0226,.0478* .0214 .Q054.0142 .0020DAB to Per.Ord. - Int.Per. .0006.0034 .0038 .0074 .0214 .0450 ' .0658 .0362 ANA .0194 .0106 .0022 ul.., 1 Per. - Per.Ord. .0020.0006 .0064,.0042 .0138.0090, ,0226.0222 .0612.0500 .0624.0414 .0264,.0318 .0112.0182 .0050,9126 .0012.0020 Interval OrdinalSample A Percentile Descriptions of Samples Interval 50.147OrdinalSample B Percentile50.246 MeanSDMeans of of Meansof SDs Means 50.019 1.0493.727 50.049 3.7921.047 50.107 9.2282.530 50.033 2.0797.391 7.4182.076 9.1732.484 MeanSD of SDsSkews 0.9871.108 0.6190.798 0.0091.190 0.6010.9752.233 0.5940.9392.049 -0.025 0.3831.169 MeanSD of KurtosisSkews 1.7260.5130.601 -0.399 1.1570.487 0.438-1.0670.391 1.7140.479 1.6810.155 -1.037 0.430 OBTAINED PERCENTAGES OF t VALUESPositive FOR GIVENSkewed LEVELS OF SIGNIFICANCE FOR (N -15 ) andPositive Skewed(N =15 ) DISTRIBUTIONS TABLE R - 76 . A Scales B . .0010 .0050 .0100 .0250 Levels of Significance .0500 .0500 .0250 .0100 .0050 .0010 Int.Int: - Int.Ord. 0000pja .0012.0006 .0040.0020 .0164.0116 .030 no, .0646.0760* ,..0361,0440 .0170.n737 A131.0100 .0034.0036 Ord.Int. - -Int. Per. .0024 ,cula.0006 .0020.0204 .0106.0392 .0306*.0728* .0812*.0334 .0466*.0142 .0248.0042 .0024.0152 .0042.0006 Ord.Ord. - -Ord. Per. A000.0018.0000 .0096.0014 .0174.0036 .0356.0146 .0644.0330 .0374.0690 .0182.0380 .0052.0188 .0034.0116 .0008.0038 Per.Per. - -Ord. Int. .0000.0000 .0012.0010 .0034.0026 .0152.0116 .0350.0316 .0662.0768* .0382.0438 .0178.0212 .0100.0138 .0038.0040 ' Per. - Per.. .0016 .0072 Sample A .0130 .0296 Descriptions of Samples .0592 .0434 .0198 Sample B .0080 .0036 .0012 SDMeans of Meansof Means Interval49.978 1.051 50.011Ordinal 1.053 Percentile 50.008 1.270 Interval 50.056 2.033 Ordinal50.190 2.039 Percentile 50.123 1.217 MeanSD of ofSDs SkewsSDs 0.9871.1133.700 0.6250.7973.773 0.0114.6020.581 0.9952.2277.473 0.9532.1267.526 -0.020 4.6080.582 SDMeanSD of of Kurtosis SkewsKurtosis '0.531 1.7310.607 -0.370 1.1600.492 -1.058 0.4180.392 1.7060.5120.592 1.6880.1880.593 -1.052 0.4090.374 OBTAINED PERCENTAGES OF t VALUES FOR TABLE B - 77 GIVEN LEVELS OF SIGNIFICANCE FOR Scales Positive Skewed (N w3A ) andPositive Skewed(N Levels of Significance .0500 .0500 =30) DISTRIBUTIONS .0250 .0100 .0050 .0010 Int. - Int. A B _norm.0010 .0050 nn7n .0028.0100 .0138.0250 .0326 .0748* .0462* '.0186 .0220 .0108.0148 .0030.0042 Int. - Per.Ord. .0015.0002 = .0228 .0086 .0164 .0369.0198 ak.0646 .0342.0618 .0498*.0168.0366 .0252.0058 _.0014 .0162 .0058.0002 Ord. - Ord.Int. .0000.0000 .0016.0018, .0038.0032 .0158.0010 ,012 .0362 26480774* .0378 .0224 .0024.0132 .0036.0002 eo Per.Ord. - Int.Per. .0000.0016 .0014.0066 .0024.0128 .0108.0288 .0306*.0574 .0746*.0410 .0204.0450* .0264.0074 .0152 .0042 Per. - Per.Ord. .0008.0000 .0046.0014 .0030.0099 .0250.0146 Ayr.0360 .0442.0538 .0716.0376 .00R4.0202 .0044.0130 .0004.0038 Interval OrdinalSample A Percentile Descriptions of Samples Interval OrdinalSample50.130 B Percentile50.102 MeanMeansSD of of MeansSDs Means 50.008 3.8600.725 50.042 0.7213.893 50.049 4.7110.860 50.006 7.6741.475 7.7051.469 4.6920.873 MeanSD of SDsSkews 1.2250.821 0.7160.580 0.0040.408 1.6911.218 0.5641.5781.143 -0.017 0.2660.403 MeariofSDSD of of Skews Kurtosis 0.5622.3131.494 -0.095 0.4341.478 -1.140 0.2630.257 0.5702.3451.443 2.2491.011 -1.115 0.260 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN TABLE B - 78 LEVELS OF SIGNIFICANCE FOR Scales Positive Skewed (N = 5 .0250 ) and Positive SkewedN = 15) Levels of Significance .0500 .0500 .0250 DISTRIBUTIONS .0100 .0050 .0010 Int. - Int. A B Ann().0010 .0006.0050 .0014.0100 .0124 .0334 .0646 .0258.0360 .0172.0124 .0098.0080 .0026.0012 Int. - Per.Ord. nnn,nnn, .0006.0008 .0010.0018 .0018*.0144 .0056*.0400 .0062*.0530 .0022* .0230.0006 .0004.0136 .0048.0002 Ord. - Int.Ord. -QOM.onn9 .0010 .0038.0038 .0180.0170 .0417.0366 .0732*.0568 .0312.0406 .0006.0150 .0004.0088 .0002.0034 to Per.Ord. - Int.Per. -MU.0558* .0868*.0006 .1044*.0010 .1350*.0018* .1700*.0052* .1818*.0062* .1404*.0020* .1074* .0870* .0582* co Per. - Per.Ord. .0008.0562* .0034.0872* .0112.1040* .1356*.0250 .0490.1720* .1814*.0484 .0256.1402* .0098.1070* .0064.0866* .0578*.0010 Interval OrdinalSample A Percentile Descriptions of Samples Interval OrdinalSample50.048 B Percentile 50.342 MeansSD of of Means Means 50.021 1.7963.213 50.052 1.7833.350 50.36624.87212.792 50.013 3.7111.058 1.0493.784 27.609 7.527 MeanSD of ofSDs SkewsSDs 1.6610.430 0.3081.299 -0.0076.848 0.9771.1220.608 0.8030.4920.616 0.0010.3873.480 SDMean of ofKurtosisSkews Kurtosis -0.907 0.6100.596 -0.993 0.6091.134 -1.102 0.6000.529 0.5071.745 -0.393 1.183 -1.065 0.428 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN TABLE B - 79 LEVELS OF SIGNIFICANCE FOR A Scales B .0010 Positive Skewed (N =5 .0050 .0100 .0250) andPositive Skewed(N =15 ) Levels of Significance .0500 .0500 .0250 DISTRIBUTIONS .0100 .0050 .0010 Int. - Ord.Int. .0004.0000 .0014.0016 .0032.0020 .0136.0118 .0402.0354 ..9528*.0564 .0Q36*.03020180 ..0144-nu .0010 -DMA.0002.0066 .0002.0020 Ord.Int. - Int.Per. .0000.0000 .0018.0004 .0044.0012 .0170.0046* .0400.0124* .0784*.0144* .0452* .0156.0238 .0084.0138 .0028.0052 Ord. --.Ord. Per. .0000.0004 .0004.0018 .0012.0042 .0050*.0170 .0114*.0436 .0132*.0630 .0044*.0350 .0016 .0002 .0308*.0002 Per. - Int.Ord. .0242*.0252* .0462*.0456*. mg.0610* .0946*.0932* ,2112*.1346* .1424*.1486* .1048*.1092* .0712*.0766* .0528*.056* .0014.027e, Per. - Per. .0008 Interval .0050 OrdinalSample A,QQ/Q Percentile.0272 Descriptions of Samples Alm ,0522 Interval .0290 OrdinalSample B .0106 Percentile .Q052 MeansSD of of Means Means 50.030 1.827 50.053 1.810 50.108 4.322 49.972 1.036 50.010 1.038 50.030 9.1962.499 MeanMeanSD of ofSDsSDs Skews 0.4381.6303.224 0.3131.2713.360 0.0032.2678.300 0.9711.1193.678 0.6100.8073.759 0.0051.190 MeanSDSD of of Skews Kurtosis -0.911 0.5920.604 -1.007 0.8000.606 -1.105 0.6000.526 1.7130.4880.597 -0.406 0.4841.153 -1.059 0.4340.386 TABLE B - 80 OBTAINED PERCENTAGES OF tPositive VALUES FORSkewed GIVEN LEVELS (N =5 ) antPositive Skewed N =15 OF SIGNIFICANCE ) DISTRIBUTIONS FOR Int. - Int. A Scales B .0000.0010 .0006.0050 .0032.0100 .0100.0250 Levels of Significance .0500.0344 .0626.0500 .0360.0250 .0174.0100 .0104.0050 .0034.0010 Int. - Per.Ord. .0000.0002 .0014.0016 .0040.0036 .0118.0140 .0352.0384 .0314.0532 .0142.0270 .0052.0116 .002k0064 .0022.0004 Ord. - Int.Ord. .0000 .0014.0016 .0052.0044 .0160.0132 .0436.0394 .0604.0754* .0326.0420 .0226.0158 .0136.0082 .0032.006'. to Per.Ord. - Int.Per. .0014.0002 .0072.0022 .0046.0124 .0328.0130 .0608.0358 .0982*.0360 .0656*.0162 .0346*.0056 .0030.0230 .0108.0006 0co 1 Per. - Ord. .0012 .0076 .0116 .0344 .0638 .0850* .0502* .0250 .0056.0164 .0016.0064 Per. - Per. .0004 Interval .0046 OrdinalSample A .0086 Percentile.0242 Descriptions of Samples .0546 .0530 Interval .0270 OrdinalSample B .0108 Percentile MeanMeansSD of of MeansSDs Means 50.023 1.8003.204 50.058 3.3421.795 50.065 2.1384.126 50.011 3.7121.032 50.047 1.0303.790 50.055 4.6221.243 MeanSD of SDsSkews 0.4351.678 0.3091.319 0.0011.159 0.9681.106 0.6050.793 -0.004 0.3830.586 MeanSD of KurtosisSkews -0.918 0.5960.602 -1.012 0.8240.603 -1.123 0.5400.589 0.4730.5971.711 -0.421 0.4861.161 -1.077 0.418 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN TABLE B - 81 LEVELS OF SIGNIFICANCE FOR Scales .0010 Positive Skewed (N =15) and Positive SkeweeN.0050 .0100 .0250 Levels of Significance .0500 .0500 =30) DISTRIBUTIONS .0250 .0100 .0050 .0010 Int. - Ord.Int. A B .0000 0000 Ana- 0018 ,0132ADO -01132.0242 .0532_n459 0412n &sty .0208QUA .002JIM .0036.0050 .0002.0001 Ord.Int. - Per.Int. .0000.0004 MIL.0016.0028 .0050.0082 .0174.0222 .0414,.0472 .0560,.0290* .0304.0122 .0130.on47 0918fflia ,0016.0000 Ord.Ord. - -Ord. Per. .0004.0000 .0024.0036 .0070.0074 .0210.0220 .0422.0478 .0324.0490 .0156.0248 0100000 .0028.0044 .0002.0004 Per. - Int.Ord. .0010.0006 .0062.0042 .0108.0090 .0272.0298 .0576.0520 .0716*.0624 .0376.0420 .0172.0202 .0120.0100 ,0038,.0030 Per. - Per. .0004 .0066 Sample A .0104 .0270 Descriptions of Samples .0502 .0464 .0234 Sample B .0096 .0044 .0002 MeansSD of of Means Means Interval49.979 1.022 50.016Ordinal 1.021 Percentile 50.021 1.233 Interval50.003 0.718 Ordinal50.035 0.719 Percentile 50.038 0.871 MeanSD of SDsSkews 0.9701.0923.687 0.6100.7803.769 0.0080.5804.609 1.2330.8233.870 0.7240.5833.900 0.0080.4004.714 MeanSD of KurtosisSkews 0.4710.599 1.724 -0.417 1.1610.483 01.071 0.4270.379 2.3901.5260.579 -0.064 1.5370.451 -1.137 0.2580.268 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE TABLE B - 82 FOR A Scales B .0010 Positive Skewed .0050 .0100 N = 5) and Positive Skewer .0250 Levels of Significance .0500 .0500 = 15) .0250 DISTRIBUTIONS .0100 .0050 .0010 Int. - Ord.Int. .0000 .0000 .0000 .0000*.0002* .0010*.0008* .0478.0352 .0238.0190 .0076M86 .0050.0044 .0018.0004 Int. - Per. .0000 .0002 .0002 .0002* .0024* .0178' .i. .0060 .0014 .0002 Ord.Ord. - -Ord. Int. .0000 .0000 .0000 .0000*.0002* .0012*.0008* .0488.0366 ,alak.0262 Ania.0124.0088 .0058.0042 .0020.0018 ms Ord. - Per. .0000 .0002 .0002 .0004* .0028* .0178* .0068 .0018 .0014 .0002 naco 1 Per. - Ord.Int. .0090.0064 .0218.0180 .0324*.0256 .0532*.0506* .0804*.0776* .1422*.1122* .0950*.0744* .0592*.0438* .0446*.0312* .0216*.0130 Per. - Per. .0006 .0040 Sample A .0084 .0148 Descriptions of Samples .0270* .0732* .0400 Sample B .0164 .0114 .0028 SDMeans of Meansof Means Interval49.998 1.792 50.025Ordinal 1.783 Percentile 12.90150.156 Interval49.905 5.186 48.384Ordinal 4.298 Percentile 46.299 7.952 Ci MeanSDMean of of Skews SDs SDs 0.4401.6523.204 0.3201.3013.347 24.884 0.0137.018 18.3580.9895.566 15.525 0.8113.546 29.160 0.0773.724 SDMeanSD of of Kurtosis SkewsKurtosis -0.918 0.5900.595 -1.003 0.8240.604 -1.119 0.5250.594 1.7430.5070.602 1.2710.0580.508 -1.0840.4390.388 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN TABLE B - 83 LEVELS OF SIGNIFICANCE FOR A Scales B .0010 Positive Skewed .0050 .0100 (N = 5 ) andPositive Skewed(N .0250 Levels of Significance .0500 .0500 =15 )DISTRIBUTIONS.0250 .0100 .0050 .0010 Int. - Ord.Int. .0000.0000 420.11.0000 .0002.0000 .0004* .0022* ,0115.0412 .0196 .0086.0020 .0052.0042 .0010.0014 Ord.Int. - -Int. Per. .0000.0002 .0000.0006 .0000.0016 .0048*.0004* Ala!Aoap*.0026* .0442.009,2* .0208.0048*171 AulaAna .0060.0002 A000.0012 Ord.Ord. - -Ord. Per. .0002,.0000 ,0006,.0000 Agoll.0014, .0044QQa* .0030*0126* Aue.0360 .0046*.0184 .0010.0092 ,0002Apkia .0000.0014 tl: Per. - Int, ,0012, .0060 .0138 .0322 .0626 .0968* .0600* .0348* .0232 .0094 L.)co 1 Per. - Ord.Per. L0010.0010, .0050.0062 .0104.0140 .0254.0336 ,0640.0512 .0486.0880* ,054*.0244 ,0096.0318* .0046.0216 .0004.0074 Interval OrdinalSample A Percentile Descriptions of Samples Interval OrdinalSample B Percentile 50.198 MeanMeansSD of of MeansSDs Means 50.026 3.2261.812 50.051 3.3601.802 50.106 8.2864.307 50.017 7.4332.094 50.129 7.4642.076 9.1772.481 MeanSD of SDsSkews 0.4371.687 0.3191.324 0.0032.335 ; 0.6150.9982.281 0.6040.9572.112 -0.012 0.3771.188 MeanSDSD of of Skews Kurtosis -0.909 0.6080.605 -0.991 1.7270.611 -1.107 0.5990.530 0.5451.797 0.2061.750 -1.046 0.416 TABLE B - 84 OBTAINED PERCENTAGES OFPositive t VALUES Skewed (N = 5 ) andPositive Skewed(N FOR GIVEN LEVELS OF SIGNIFICANCE = 15 ) DISTRIBUTIONS FOR Int. - Int. A Scales B .1100.0010 .0000.0050 .0002.0100 .0006*.0250 Levels of Significance ,0012*.0500 .0187.0500 .0186.0250 .0090.0100 .0050 .0014.0010 Int. - Ord.Per. Anaa.0004 .0038.0000 .0060.0004 .0008*.0148 ,0040*.0322 .0330.0306* .0172.0130 .0070.0042 .002Q.0038 .0006.0Q12 Ord. - Int.Ord. Ama.0000 .0002.0000 .0004.0002 .0008*.0006* .0040*.0036* .0346.0422 .0200. 117.2. AMA.0070 .0044.0052 ..0018,.0016 as Ord.Per. - -Per. Int. .0000.0006 .0040.0000 .0004.0064 ,0156.0024* .0088*.0420 .0474.0324 .0252.0142 .0046.0104 .0072.0024 .0022.0004 co Per. - Per.Ord. .0014.0000 .0064.0004 .0ii,.0004 .0280.0026* .0576.0098* .0484.0410 .0252.0220 .0104.0090 .0052.0052 .0024.0010 Interval OrdinalSample A Percentile Descriptions of Samples Interval 50.167OrdinalSample B Percentile 50.111 MeansMeanSD of ofof Means MeansSDs 49.967 1.7823.172 49.994 1.7793.316 49.997 4.1282.147 50.037 7.4302.126 7.4702.127 4.5901.263 MeanSD of ofSDs Skews 0.4341.630 1.2830.309 1.1540.013 0-9952.256 0.6040.9532.119 -0.022 0.3890.589 MeanSDSD of of Skews Kurtosis -0.919 0.6000.594 -1.005 0.6041.031 -1.117 0.5960.531 0.5420.6071.749 1.7200.208 -1.034 0.436 OBTAINED PERCENTAGES OF t VALUES FOR TABLE B - 85 GIVEN LEVELS OF SIGNIFICANCE FOR Scales .0010 Positive Skewed .0050 .0100 (N =15 ) and positive Skewed(N =30) .0250 Levels of Significance .0500 .0500 .0250DISTRIBUTIONS .0100 .0050 .0010 Int. - Ord.Int. A B .0000 .0000 .0004.0002 .0028*.0018* .0128.0096* .0322.0398 .0152.0212 .0074.0058 .0034.0026 .0008.0010 Ord.Int. - Int.Per. .0006.0000 .0000.0034 .0004.0084 .0018*.0250 .0104*.0502 .0424.0282* .0224.0102 .0076.0030 .0040.0010 .0006.0002 Ord.Ord. - -Ord. Per. .0006.0000 .0000.0028 .0006.0078 .0228.0024* .0448.0136* .0338.0316 .0120.0168 .0038.0066 .0016.0032 .0004.0006 cow Per. - Int.Ord. .0000 .0006.0002 .0010.0008 .0036*.0052* .0180*.0150* .0384.0480 .0192.0242 .0100.0074 .0032.0048 .0008.0012 VI Per. - Per. .0014 .0062 Sample A .0120 .0304 Descriptions of Samples .0562 .0460 .0180 Sample B .0066 .0038 .0006 ry,,.A., Interval Ordinal Percentile Interval49.995 Ordinal50.130 Percentile 50.098 MeanSDMeans of of Meansof SDs Means 50.025 1.0413.733 50.059 3.7991.036 50.063 4.6201.246 7.6711.453 7.7141.454 4.6980.869 MeanSD of SDsSkews 0.9791.115 0.8000.4830.611 -0.004 0.3840.582 0.5741.6441.224 0.5751.5721.154 -0.020 0.4040.264 MeanSD of KurtosisSkews 1.7170.5030.598 -0.405 1.151 -1.065 0.426 2.3771.477 2.3241.068 -1.115 0.260 TABLE B - 86 OBTAINED PERCENTAGES OFPositive t VALUES Skewed FOR GIVEN (N = 15 ) and Positive Skewed(N = 5 LEVELS OF SIGNIFICANCE FOR ) DISTRIBUTIONS A Scales .0010 .0050 .0100 .0760*.0250 Levels of Significance .0500 .0500.2570* .2156*.0250 .0100.1670* .1418*.0050 .0950*.0010 Int.Int. - -Int. Per.Ord. .0106.0138 .0348*.0240.0292* -.015D,.0450* .0912*.0557* .1168*tale .2480*.2920* .2446* .1492*.1928* .1612* 1252* .0834*.1074 * Ord. - Int.Ord. .0355*.0100.0130 .0246*.0288* ,aza*.0348*11428* .0560*.0740* .0838*.1128* ,2222*,zale .2150*.2456* .1930*log* .1406*.1616* .1090*.0952* Per.Ord. - Int.Per. .0348*.0002 .0552*.0014 .0030.0682* .0904*.0086 .0228*.1172* .0216*.2502* .0094.1966* .0026.1500* .0012.1250* .0002.0836* Per. - Ord.Per. .0002.0012 .0036.0010 .0068.0020 .0052*.0160 .0132*.0300* .0828*.0224* .0468*.0086 .0222.0030 .0014.0104 .0034.0002 Interval OrdinalSample A Percentile Descriptions of Samples Interval 48.380OrdinalSample B Percentile 46.255 MeanSDMeans of of Meansof SDs Means 50.000 3.7311.039 50.030 3.7941.035 27.69650.164 7.427 49.86515.877 8.729 13.659 7.319 26.42013.524 MeanSD of of SDs Skews 0.9931.126 0.8130.624 0.006'2).539 0.4358.019 0.3825.7560.596 0.0460.5917.255 MeanSD of KurtosisSkewsKurtosis 0.6090.5511.741 -0.375 0.4861.164 -1.063 0.4350.386 -0.929 0.5760.592 -0.952 0.564 -1.123 0.525 OBTAINED PERCENTAGES OF t VALUES FOR PositiveGIVEN LEVELS Skewed OF (N = 15) andPositive Skewed(N =5 TABLE B - 87 SIGNIFICANCE) DISTRIBUTIONS FOR Int. - Int. A Scales B .0070.0010 .0192.0050 .0312*.0100 .0580*.0250 Levels of Significance .0500.0926* .1448*.0500 .0940*.0250 .0100.0550* .0050.0360* .0010.0140 Int. - Ord. .0078.0312* .0566*.0246* .0740*.0352* .1144*.0642* .1566*.1004* .1178*.1328* .0812*.0924* .0524*.0574* .0400*.0404* .0224*.0158 Ord.Int. - -Ord.Int. Per. .0056.0064 .0174.0212 .0334*.0274 .0578*.0510* .0934*.0880* .1352*.1430* .0952*.0980* .0564*.0542* .0378*.0342* .0116.0100 os Per.Ord. - -Int. Per. .0294*.0000 .0014.0520* .0692* .1078* .1486* .0302*.1188* .0124.0812* .0534*.0038 .0404*.001a .0004.0218* -4co Per.Per. - -Ord. Per. A0011ADM ,0014 Ana.0124.0052 ,0136.0254.0150 jau.0496.0336 .0464.0290* .0232..0126 .0074.0040 .0050.0010 .0008.0002 Interval ,ffla OrdinalSample A Percentile Descriptions of Samples Interval OrdinalSample50.107 B Percentile 50.237 MeanSDMeans of ofMeansof SDs Means 49.995 3.7101.031 50.027 3.7831.025 50.064 9.2302.464 49.992 6.3183.503 6.4003.513 8.2234.225 MeanSD of SDsSkews 0.9761.109 0.6110.797 0.0061.162 0.4373.212 0.5043.045 -0.009 0.5812.325 SDMean of ofKurtosisSkews Kurtosis 1.7110.4820.595 -0.416 1.1640.484 -1.069 0.4460.383 -0.9250.5730.588 -2.106 0.616 .585 -1.119 0.511 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR TABLE B - 88 A Scales B .0010 Positive Skewed .0050 .0100 (N = 15) and Positive Skewed(N =5 ) DISTRIBUTIONS .0250 Levels of Significance .0500 .0500 .0250 .0100 .0050 .0010 Int.Int. - -Ord. Int. .0092.0082 juaz 0230 .0348*.0304* .0654*.0578* ,a9$2*.Ole .1376*.1524* .0948*.1006* .0602*.0600* .0432* 0370* .0132 Ord.Int. - -Int. Per. .0064.0096 Aliall 0256* .0260.0382* .0530*.0656* -01286,.0866* ..1532* .0542 .1008*.0280 Aka.0590* .0356*.0166 QUA.010Z.0006 Ord. - Per.Ord. .0040.0074 .0170.0194 .0266.0308* .0516.0600* * .0940* .0570.1410* .0320.0954* .0124.0584* .0056.0414* .0012.0142 Per.Per. - -Ord. Int. .0032.0020 .0138.0110 .0222.0184 .0442*.0382 .0748*.0676t085e .1122*.1196* .0686*.0730* .0162*.01511* .0210.0216 .0060.0054 Per. - Per. .0008 .0044 Sample AAlai .0256 Descriptions .0520 of Samples .0454 .0218 Sample B .0076 .0044 .0010 SDMeans of Meansof Means Interval 50.003 1.042 Ordinal50.037 1.034 Percentile 50.047 1.244 Interval49.973 3.562 Ordinal50.099 3.563 Percentile 50.074 2.128 MeanSD of SDsSkewsSDs 0.9701.1253.706 0.6090.8063.779 -0.000 0.5824.606 0.4403.2816.379 0.5086.4523.116 -0.005 1.1484.146 MeanSD of SkewsKurtosis 1.7320.4860.607 -0.404 1.1800.493 -1.073 0.4120.382 -0.920 0.5830.600 -1.087 0.619 .525 -1.109 0.5250.593 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE TABLE B - 89 FOR Scales B Positive Skewed (N = 30) and Positive Skewed(N.0050 2,15) .0100 .0250 Levels of Significance .0500 .0500 .0250 DISTRIBUTIONS .0100 .0050 .0010 Int. - Ord.Int. A .0026_nwo.0010 .0120.0084 .0192.0162 .0436.0370 .0790*.0690 .0982*.1134* .0732*.0622* .0364*.0422* .0256*.0272* ,012,2.0108 Ord.Int. - -Int. Per. .0016.0032 .0084.0142 .0144.0248. .0344.0470* .0652.0784* .1180*.0410 .0768*.0184 .0448*.0080 .0292*.0050 .0132.0010 Ord. - Per.Ord. .0028.0016 .0110.0106 .0182.0166 .0420.0412 .0690.07444 .0484.1008* .0222.0662* .0096.0398* .0052.0280* .0010.0118 .4,cow 1 Per. - Ord.Int. .0014.0010 .0080.0058 .0138.0122 .0322.0268 .0670.0582 .0918*.1028* .0546*.0638* .0328*.0358* .0210.0250* .0082.0066 Per. - Per. .0010 .0050 Sample A .0094 .0254 Descriptions of Samples .0508 .0416 .0200 Sample B .0094 .0036 .0006 MeansSD of of Means Means Interval50.003 0.719 50.035Ordinal0.718 Percentile 50.041 0.874 Interval50.043 2.060 50.172Ordinal 2.065 Percentile 50.124 1.235 MeanSD of SDsSkewsSDs 1.2340.8303.862 0.7270.5893.896 0.0110.4054.703 0.9872.2387.424 0.9472.1177.477 -0.024 0.5924.592 MeanSD of KurtosisSkews 2.4171.5350.584 -0.056 1.5500.454 -1.135 0.2610.269 1.7390.5160.603 1.7040.1900.598 -1.044 0.4450.382 TABLE B 90 OBTAINED PERCENTAGES OFPositive t VALUES Skewed FOR GIVEN (N = 5 ) andNeaative Skewed(N = 5 LEVELS OF SIGNIFICANCE FOR ) DISTRIBUTIONS Int. - Int. A Scales B .0118.0010 .0326*.0050 .0460*.0100 .0752*.0250 Levels of Significance .1102*.0500 .0174*.0500 .0250 .0100 .0050 .0002.0010 Int.Int. - -Per. Ord. .0090.0092 .0222.0230 .0284.0360* .0466*.0596* .0672.0888* .0724*.0240* Aialeau&.0094 .0304*021.0030 l=.0182.0010 .0002.0104 .0086 .0242* .0382* .0604* .0932* .0230* .0102 .0028 .0018 .0006 Ord.Ord. - -Int.Ord. Per. .0070.0096 .0222.0182 .0286.0292* .0462*.0482* .0676.0760* .0718*.0282* .0490*.0138 .0308*.0048 .0186.0024 .0104.0006 .0= Per. - Ord.Int. .0090 .0218.0216 .0298*.0310* .0468*.0470* .0750*.0740* .0686.0674 .0468*.0462* .0292*.0288 .0232 .0104 o Per. - Per. .0012 .0060 Sample A .0108 .0240 Descriptions of Samples .0472 .0478 .0264 Sample B .0126 .0074 .0016 SDMeans of Meansof Means Interval49.964 1.797 49.993Ordinal 1.792 Percentile 49.96612.911 Interval50.013 1.777 49.951Ordinal 1.762 Percentile 12.81149.622 MeanSD of of SDs SkewsSDs 0.4361.6283.171 0.3171.2783.319 24.801 0.0136.953 -0.429 1.6283.191 -0.308 1.2703.317 24.8450.0066.888 MeanSD of KurtosisSkews -0.913 0.6010.600 -1.016 0.8900.604 -1.107 0.5280.598 -0.932 0.5930.601 -0.967 1.4640.604 -1.126 0.5250.588 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN TABLE B - 91 LEVELS OF SIGNIFICANCE FOR ) DISTRIBUTIONS A Scales B .0010 Positive Skewed (N = 5 ) .0050 .0100 .0250 andNeRative Skewed(N =5 Levels of Significance .0500 .0500 .0250 .0100 .0050 .0010 Int. - Ord.Int. ,aug.0100 .0260*nue ,0380*,0497* .0618* f177A .0944*1126,* .0242*.0206* _..022Q.00* .0032.0010 -nolo.0004 .000? 0009 Int. - Per. .0092.0066 .0156.0260* .0380*.0246 ,0424,.0636* ,0968*.0686 .0264*.0648 .0106.0396 ,0224212 .0134 Anao .0054 Ord. - Int.Ord. .0058.0062 .0128.0192 .0230.0312* .0402.0514* ,0664.0806* .0346 .0398.0158 A042.0216 OM_silma .0140 .0052.nno, tr Per.Ord. - Int.Per. .0060 .0 56 .0228.0202 .0394.0380 .0612.0642 -ow .0638..0616 .0374.0390 _Jima .0204 .0114.0134 ,fflia.0048 1)1-. Per.Per. - -Ord. Per. .0048.0012 A130,0064 ,0134 .0272 Descriptions of Samples .0512 .0572 .0296 .23.68 .0084 .0024 7..a Interval49.997 50.032OrdinalSample A Percentile 50.072 Interval 50.037 49.978OrdinalSample B Percentile 49.925 MeansMeanSD of of ofMeans MeansSDs 3.2041.777 1.7733.353 8.3054.241 1.7963.157 1.7813.281 4.3142.3208.242 MeanSD of SDsSkews 0.4391.646 0.3161.292 0.5940.0062.286 -0.417 0.6031.635 -0.298 0.6061.285 0.5950.013 MeanSD ofSD of Skewsof Kurtosis Kurtosis 0.6000.5850.908 -1.001 0.6031.162 -1.111 0.525 -0.929 0.592 -0.948 1.775 -1.116 0.529 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE TABLE _li_r92 FOR A Scales B .0010 Positive Skewed .0050 .0100 (N = 5 ) andNgsalisaskeseed(N m) DISTRIBUTIONS .0250 Levels of Significance .0500 .0500 .0250 .0100 .0050 .0010 Int. - Ord.Int. ,0972.0110 .0216.0284* .0354*.0454* .0606* ,020eJ.148* .0230* .mal.0068 .0036.0018 .0014.0010 .0006.0004 Ord.Int. - -Int. Per. .0074.0044 jun.0224 .0332*.0216 ,0592*,0402Alle .0954*.0636 AnaAug.0240* .0104.0196 .0032.0082 .0014.0046 .0004.0008 Ord. - Per.Ord. .0034.0054 .0090.0172 .0172.0266 .0314.0472* .0564.0766* .0434.0304* .0218.0132 .0112.0042 .0048.0022 .0010.0006 1, Per. - Ord.Int. .0032.0048 .0096.0120 .0192 .0310.0358 .0550..0636 .0450.0400 .0230.0202 .0098.0088 .0056.0048 .0012.0010 Per. - Per. ,0911 .0060 Sample AAix.0094 .0224 Descriptions of Samples .0468 .0496 .0272 Sample B .0128 .0076 .0022 SDMeans of Meansof Means Interval 50.036 1.798 50.082Ordinal 1.804 Percentile 50.099 2.156 Interval 50.036 1.787 Ordinal49.974 1.773 Percentile 49.962 2.143 MeanSD of SDsSkewsSDs 0.4291.6203.200 0.3041.2703.344 -0.010 1.1334.134 -0.423 1.6523.175 -0.300 1.2903.294 0.0171.1514.121 MeanSDSD of of Skews Kurtosis -0.912 0.5930.605 -0.980 0.6111.594 -1.1060.5340.599 -0.922 0.5980.603 -0.932 2.2320.607 -1.115 0.5290.590 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF TABLE B - 93 SIGNIFICANCE FOR Scales Positive Skewed .0050 .0100 (N = 5 ) andNegative Skewed(N .0250 Levels of Significance .0500 .0500 = 5 ) DISTRIBUTIONS.0250 .0100 .0050 .0010 Int. - Int. A B .0292*.0010 .0608*.0562* .0762*.0738* .1068*.1108* .1532*147R* .0220*.0248* .0104 .0038.0034 _nom.0022 .0002.0000 Int.Int. - Ord.- Per. ,01411.0306*.0276* .0320*.0544* .0726*.0428* ,0678*21056* .1466*.0962* .0250*.0546 .0360 .0108 .0032.0214 .0156.0018 .0000.0066 Ord. - Int.Ord. .0146.0280* .0324*.0566* .0432*.0760* .0672*.1092* .1512*.0956* .0544.0228* .0098.0360 .0214.0040 .0156.0022 .0068.0002 al Per.Ord. - Per.Int. .0054 .0138 .0188 .0396.0355 .0660.0618 .0480.0490 .0274.0256 .0120.0106 .0056.0064 .0018.0020 u,(...) Per.Per. - -Ord. Per. .0036.0066 .0096.0144 .0194.0210 .0344 Descriptions of Samples .0588 .0428 .0230 .0096 .0042 .0006 Interval OrdinalSample A Percentile . Interval 50.030 OrdinalSample51.192 B Percentile 52.623 MeansMeanSD of of ofMeans Means SDs 49.984 1.7823.191 50.017 1.7813.339 50.10812.81924.933 15.6999.074 13.297 7.350 25.88313.759 MeanSD of ofSDs Skews 1.6240.434 0.3081.279 -0.000 6.995 -0.428 8.1520.596 -0.376 5.6740.596 -0.028 0.6007.195 SDMean of ofSkewsKurtosis Kurtosis -0.897 0.6160.603 -0.986 1.2860.606 -1.105 0.6020.529 -0.933 0.577 -O.963 0.651 -1.118 0.530 OBTAINED PERCENTAGES OF t VALUES FOR TABLE B - 94 GIVEN LEVELS OF SIGNIFICANCE FOR Scales B .0010 Positive Skewed .0050 .0100 (N = 5 ) andNegative .0250 Levels of Significance .0500 Skewed(N .0500 =5 ) DISTRIBUTIONS.0250 .0100 .0050 .0010 Int. - Ord.Int. A .0188.0146 .0346*.0400* .0544*.0516* .0840*.0848* .1186*.1234* .0212.0202* * .0050*.0076 .0026.0022 .0010.0004 .0000 Int. - Per. .0108_ons, Aia6..0278* .0424*_n714 , ....03afi.0746* .1114* n646 _1153fi.0190* .0060 nls, _aim .0024 _..0324 .0010 .0000jaciza Ord. - Int.- Per.Ord. .0146.0048 .0116.0318* .0210.0464* .0376.0744* .0602.1104* .0576.0216* .0350.0090 .0198.0034 .0110.0010 .0024.0002 ul Per. - Int. .0048 .0134 .0216 .0400 .0670 .0406.0408 .0204 .0078.0082 .0046.0036 .0006.0008 .r.- Per. - Ord.Per. .0026.0046 .0072.0136 .0126.0208 .0262.0396 .0474.0678 ,0500 .0268 .0122 .0060 .0018 Interval OrdinalSample A Percentile Descriptions of Samples Interval OrdinalSample B Percentile 49.904 MeanSDMeans of ofMeansof SDsMeans 49.967 1.7963.168 50.005 3.3221.798 50.007 8.2624.310 49.910 6.3863.588 49.982 6.3503.543 4.2708.245 MeanSD of ofSDs Skews 0.4341.648 0.314.1.301 0.0072.277 -0.425 3.295 -0.485 3.107 0.5850.0122.320 MeanSDSD of of Skews Kurtosis -0.910 0.6040.600 -1.014 0.8440.608 -1.108 0.5950.524 -0.9330.5920.572 1.3940.633 .556 -1.116 0.515 TABLE B - 95 OBTAINED PERCENTAGES OF t VALUES FOR GIVENPositive Skewed (N = 5 ) andNeRative Skewed(N = 5 ) LEVELS OF SIGNIFICANCE FOR DISTRIBUTIONS Int. - Int. A Scales B .0120.0010 .0324*.0050 .0500*.0100 .0858*.0250 Levels of Significance _7964*.0500 _0200*.0500 .0072.0250 _no',.0100 .0050 0008 .0002.0010 Int. - Ord.Per. .0034.0176 .0366*.0104 ,0166.0534* .0830*.0366 .0626.1180* .0416.0232* .0198.0098 .0094.0028 .0040.0014 .0006.0002 Ord. - Int.Ord. .0124.0094 ,0300*.0242* "LA2e.0394* .0744*.0730* .1166*.1108* .0236*.0226* .0098.0078 0022.003i .0014.._QQ08 .0002.0000 Per.Ord. - Int.Per. .0056.0032 .6126.0090 .0232.0146 .0502*.0292 ,020*.0552 .0280*.0458 ,.0098.0236, .0028.0090 .0014.0056 .0002.0000 Per.Per. - -Ord. Per. ,0028.0062, .0156.0066 0 U.0260 .0522.0244 * ,0452.0918 .0284*.0526 .0282.0122 .0132.0032 .0064.0016 .0002.0014 rs% Interval OrdinalSample A Percentile Descriptions of Samples Interval50.008 OrdinalSample50.078 B Percentile 50.015 MeanMeansSD of of Means SDsMeans 49.953 3.1571.782 49.989 1.7843.320 49.987 4.1412.148 6.3463.587 6.3273.546 4.1242.141 MeanSD of SDsSkews 0.4301.621 0.3151.285 0.0131.158 -0.431 0.5963.235 -0.500 0.6223.074 -0.009 0.5921.153 SDMean of ofKurtosisSkews Kurtosis -0.928 0.5910.596 -0.989 1.4480.599 -1.127 0.527.0.591 -0.934 0.589 -1.570 .575 -1.111 0.556 OBTAINED PERCENTAGES OF t VALUESPositive FOR Skewed GIVEN LEVELS OF SIGNIFICANCE FOR (N = 15) andNegative Skewed(N = 15) DISTRIBUTIONS TABLE B - 96 Int. - Int. A Scales B .0010 .021Q.0050 .0100 .0504*.0250 Levels of Significance .0774*.0500 .0244*.0500 .0070.0250 .0026.0100 .0016.0050 .0000.0010 Int. - Ord.Per. Mak.0044 .0056.0126 ,030*.0222 .0216.0404 .0404.064, .0322.0626 .0366.0106 .0030.0170 .0098 .0030.0002 Ord. - Ord.Int. qua.QC:..t.:.0034 .0102.0150 A)1.71.0248,.MO ,_0_426.0342 .0556.0662 .0400.0302 .0158.0104 .0042.0030 Ma.0028.0024 ,0004.0006 Per.Ord. - Int.Per. ,0020.0038 .0088.0056 .0122.0108 .0284.0210 .0506.0400 .0568.0630 .0322.0366 .0150.0176 .0074.0104 .0026.0028 a%= 1 Per. - Ord. .0038 .0088 .0120 .0280 .0500 .0582 .0324 .0152 .0070 .0020.0026 Per. - Per. .0008 Interval .0040 OrdinalSample A .0082 Percentile.0208 Descriptions of Samples .0404 .0574 Interval .0308 OrdinalSample B .0106 Percentile .0068 SDMeans of Meansof Means 50.012 1.036 50.044 1.033 50.301 7.464 49.992 1.023 49.926 1.010 27.60049.434 7.300 MeanSD of ofSDs SkewsSDs 0.9861.1183.725 0.6150.8053.789 27.654 0.0013.533 -0.969 1.1313.716 -0.611 0.8083.763 0.0173.497 SDMean of ofKurtosisSkews Kurtosis 1.7570.5350.610 -0.3831.2090.498 -1.062 0.4380.386 1.7290.4790.607 -0.406 1.1670.488 -1.078 0.4270.380 OBTAINED PERCENTAGES OF t VALUES FOR TABLE B - GIVEN LEVELS OF SIGNIFICANCE97 FOR Scales .0010 Positive Skewed .0050 .0100 (N =15 ) andNegative Skewed(N =15 .0250 Levels of Significance .0500 .0500 ) DISTRIBUTIONS.0250 .0100 .0050 .0010 Int. - Ord.Int. A B AIDA.0060 .0.2511,.0182 .0274.0390* .0506* _LIMA*.0818* .0202*Jae .01040076 .0038.0032 .0020.0008 ,00110 Ord.Int. - -Int. Per. .0028 .0080 ...0312!.0142 -WAR*.0308 .0550-0R7n* .0160 0264* .0297.041aa ,9128 .00120068 -MOO-.0020 Ord.Ord. - -Ord. Per. .0022.0040 .0082.0126 .0132.0212 .0296.0414 .0548.0702* .0584.0356 .0316.0134 .0140.0050 .0076.0030 .0022.0004 os Per. - Int.Ord. .0038.0038 .0080.0092 .0152.0166 .0296.0322 .0568.0614 .0532.0500 .0276.0246-._ jam .0110 .0068.0064 .0028.0022 Per. - Per. .0018 Interval .0058 OrdinalSample A .0106 Percentile.0258 Descriptions of Samples .0532 .0534 Interval .0262 OrdinalSample B .0110 Percentile A062 .0024 SDMeans of Meansof Means 49.989 1.041 50.019 1.038 50.037 2.502 50.033 3.6701.031 49.966 3.7221.022 49.882 9.1372.476 MeanSD of SDsSkews 0.9811.1193.711 0.6170.8083.783 0.0099.2231.169 -0.984 1.122 - 0.624 0.806 0.0051.187 SDMean of ofKurtosisSkews Kurtosis 0.5070.6051.737 -0.400 0.4871.169 -1.0660.3880.446 1.7410.5250.603 - 0.373 1.1790.485 -1.063 0.3790.440 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN TABLE B - 98 LEVELS OF SIGNIFICANCE FOR A Scales B .0010 Positive Skewed (N =15 ) andNeaative .0050 .0100 .0250 Levels of Significance .0500 Skewed(N =15 ) .0500 .0250 DISTRIBUTIONS .0100 .0050 .0010 Int. - Ord.Int. .0042.0088 .0757*0167 .0746.0150* .0464*.057A* .0740*.0862* .025.0328 * gfa.0128 .0034.0020 .0016.0010 .0000 Ord.Int. - Per.Int. .0054,.0022 .0168.0080 0136.0270 .0454*.0306 .0734*.0570 .0318.0456 .0120.0220 .0034.0086 .0016.0036 .0002.0000 Ord. - Per.Ord. .0014,.0030 .0070.0104 .0114.0194 .0248.0364 .0508.0626 .0398.0502 .0166.0264 .0056.0114 .0052.0020 .0000.0004 = Per. - Ord.Int. .0020.0026 .0068.0100 .0130.0142 .0282.0354 .0504.0566 .0494.0430 .0236.0182 .0106.0072 .0050.0036 .0002 co Per. - Per. .0014 .0050 Sample A .0096 .0204 Descriptions of Samples .Q450 .0568 .0284 Sample B .0146 .0082 .au MeansSD of of Means Means Interval 49.991 1.036 Ordinal50.022 1.029 Percentile 50.029 1.232 Interval50.005 1.040 Ordinal49.942 1.032 Percentile 49.924 1.244 MeanSD of SDsSkews 0.9761.1353.705 0.6180.8153.778 0.0080.5804.603 -0.977 1.0983.705 -0.615 0.7783.749 4.5950.0080.579 MeanSD of KurtosisSkews 1.7140.4970.602 -0.394 0.4861.164 -1.070 0.4180.379 0.6001.7140.485 -0.412 0.4851.150 -1.069 0.4270.390 TABLE B - 99 OBTAINED PERCENTAGES OF t VALUESPositive FOR Skewed (N 30 ) andNegative Skewed(N =30 GIVEN LEVELS OF SIGNIFICANCE FOR ) DISTRIBUTIONS A Scales B .0010 .0050 .0100 .0250 Levels of Significance .0500 .0500.0304* .0250.0144 .0100.0048 .0050.0016 .0010.0002 Int. - Per.Ord.Int. .0008.0024.0036 .0060.0088.0142 .0110.0174.0230 .0422.0268.0360 .0508.0598.0734* .0484.0398 .0220.0172 .0092.0056 .0042.0026 .0006.0004 Ord.Ord. - -Ord. Int. .0008.0020 .0064.0102 .0122.0160 .0366.0286 .0612.0510 .0440.0374 .0170.0214 .0066.0080 .0036.0022 .0006.0002 Per.Ord. - Int.Per. .0008.0002 .0064.0046 0098.0086 .0252.0206 .0536.0440 .0418,.0542 .0210.0276 .0086.0104 .0034.0056 .0006.0010 Per. - Per.Ord. .0002 A228..0052 Aug0178 ..sailaglia .0432 .0516.0584 .0264.0292 .0102.0142 .0066.0058 .0014 Interval OrdinalSample A Percentile 50.042 Descriptions of Samples Interval49.986 Ordinal49.922Sample B Percentile 49.899 MeanSDMeans of ofMeansof SDs Means 50.004 0.7333.859 50.036 3.8910.727 0.8664.708 0.7373.859 0.7293.861 4.7000.876 MeanSD of ofSDs Skews 0.5721.2210.839 0.4440.7160.594 0.2650.0060.399 -1.212 0.5710.827 -0.709 0.4440.379 0.2690.0170.395 SDMeanSD of of Kurtosis SkewsKurtosis 1.4752.350 -0.094 1.505 -1.139 0.253 1.4492.350 -0.113 1.508 -1.145 0.254 B - 100 OBTAINED PERCENTAGES OF t VALUESPositive FOR GIVEN Skewed LEVELS OF SIGNIFICANCE (N = 15) andNegative Skewed(N = 15) TABLE DISTRIBUTIONS FOR A c!:Stales B .0010 .0050 .0100 .0250 Levels of Significance .0500 .0500 .0250 .0100 .0050 .0010 Int. - Int. .0172 .0366* .0490* .0782* .1108* .0174*.0256* .0070.0082 .0014.0016 .0008.0008 .0002 Ord.Int. - Ord.Int.Per. .0178.0070.0200 ,0202.0456* .0488*.0300*.0606* .0764*.0594*.0956* .1086*.1012*.1364* .0250.0248* * .0084.0150 .0016.0078 .0008.0044 .0002.0010 Ord.Ord. - -Ord. Per. .0072.0192 ,0362*.0202.0436* .0306*.0586* .0592*.0928* .1010*.1338* .0256*.0172* .0160.0074 .0078.0012 .0042.0008 .0010.0002 t Per. - Int. .0040 .0082 .0144 .0316 .0558 .0490 .0248 .0076 .0020 .0006 0oa-. Per. - Per.Ord. .0034.0046 .0106.0094 .0188.0158 .0370.0438 .0798*.0668 .0340.0390 .0214.0156 .0052.0072 .0020.0026 .0004 Means of Means Interval49.982 OrdinalSample50.017 A Percentile 50.110 Descriptions of Samples Interval 50.062 OrdinalSample51.276 B Percentile 52.808 SD of Means 1.041 1.039 7.535 5.177 4.174 7.699 ) MeanSD of ofSDs SkewsSDs 0.9811.0823.696 0.6140.7723.775 27.676 0.0133.427 -0.99018.467 5.687 -0.80915.295 3.523 -0.04828.968 3.640 SDMean of ofKurtosisSkews Kurtosis 1.7120.4900.594 -0.417 0.4811.145 -1.065 0.4280.390 1.6960.4980.592 1.2270.0400.495 -1.092 0.4240.385 OBTAINED PERCENTAGES OF t VALUES FOR TABLE B - 101 GIVEN LEVELS OF SIGNIFICANCE FOR Scales .0010 Positive Skewed .0050 .0100 (N =15 ) andNeRative .0250 Levels of Significance .0500 Skewed(N .0500 =15 ) .0250DISTRIBUTIONS .0100 .0050 .0010 Int. - Int. A B .0084.0090 .0232.0218 .0348* .0570*.0576* .0962*.0906* .0238*.0262* .0090.0098 .0014.0016 .0004 .0000 Int. - Per.Ord. .0076.0018 .0190.0076 .0298*.0132 .0526*.0286 .0872*.0524 .0278*.0476 .0118.0250 .0114.0020 .0070.0004 .0000.0020 Ord.Ord. - -Int.Ord. Per. .0014.0070 .0070.0202 .0140.0310* .0276.0540* .0524.0868* .0482.0266* .0262.0094 .0124.0022 .0072.0004 .0018.0000 to t Per. - Int. .0028 .0110 .0168 .0324 .0570 .0450 .0210 .0060 .0028 .0006 1-.o1- Per. - Per. Ord. .0022.0014 ...02,14.0108 .0116.0172 .0264.0346 .0464.0602 .045Q.0528 ,012$.0280 .0112.0066 .00560022 .0004.001Q Interval OrdinalSample A Percentile Descriptions of Samples Interval OrdinalSample50.147 B Percentile 50.105 MeanSDMeans of MeansofSDs Means 50.054 3.7501.050 50.088 3.8071.054 50.195 9.2342.527 50.065 7.3702.039 7.2972.009 9.1612.445 MeanSD of ofSDs Skews 0.6040.9771.112 0.4940.6050.802 -0.009 0.3901.183 -1.004 0.6012.209 -0.966 0.6012.061 -0.025 0.3841.179 MeanSDSD of of Skews Kurtosis 1.7240.501 -0.409 1.172 -1.066 0.427 1.7620.546 0.2171.747 -1.039 0.445 TABLE B - 102 OBTAINED PERCENTAGES OF t VALUESPositive FOR GIVENSkewed CO =15 ) andNegative Skewed(N '15 LEVELS OF SIGNIFICANCE FOR ) DISTRIBUTIONS Int. - Int. A Scales B .Cilia.0010 .0236.0050 _nu,*.0100 .0250nfiu* Levels of Significance An?,*.0500 .0272*.0500 .0118.0250 .0100 .0016.0050 .0004.0010 Int. - Ord.Per. ADA.0020 .0094.0230 .0162.0358* .03460640* .1008*.0598 .0390.0270* .0202.0122 ,0032jaicja .0042.0018 .0012.0004 Ord. - Int.Ord. .0086.0088 .0192.0198 .0330*.0316* ...0588*.0612* .0932*.0944* .0286*.0270* .0120.0128 .0042.0038 ,Qua.0016 .0004.0006 Per.Ord. - Int.Per. .0040.0014 .0146.0074 .0252.0122 ,0488'.0276 .0542.0822' .0314.0446 .0222.0130 .0048.0110 .0020.0056 .0004.0014 Per. - Ord.Per. .0016.0050 .0142.0050 .0096.0242 .0238.0480* .0450.0830* .0494.0310 .0252.0142 .0118.0050 .0062.0024 _nnis.0008 Interval OrdinalSample A Percentile Descriptions of Samples Interval OrdinalSample B Percentile 50.035 MeanSDMeans of ofMeansof SDs Means 50.010 3.7181.036 50.041 3.7871.027 50.050 4.6101.231 50.049 2.0707.344 50.122 7.2712.028 4.5771.239 MeanSD of of SDs Skews 0.9811.127 0.6140.812 0.5770.002 -0.987 2.183 -0.955 0.5962.033 -0.009 0.5880.384 MeanSD of KurtosisSkews 1.7310.5070.603 -0.401 0.4851.155 -1.068 0.3870.429 0.5180.6021.731 0.2001.717 -1.037 0.447 TABLE B - 103 OBTAINED PERCENTAGES OF t VALUESPositive FOR Skewed (N =30 ) andNeeative Skewed(N GIVEN LEVELS OF SIGNIFICANCE FOR =30) DISTRIBUTIONS Int. - Int. A Scales B .0068.0010 .0188.0050 .0264.0100 .0494*.0250 Levels of Significance .0794*.0500 .0312*.0500 .0128.0250 .0100.0028 .0050.0008 .0000.0010 Int. - Ord.Per. .0064.0022 .0196.0082 .0296*.0130 .0316.0506* .0560.0844* .0418.0282* .0186.0114 .0074.0028 .0034.0008 .0006.0000 Ord. - Int.Ord. .0060.0056 .0164 .0276.0246 .0472*.0486* .0736*.0794* .0304*.0330 .0124.0138 .0032.0034 .0010.0012 .0000 to Per.Ord. - Int.Per. .0020 .0124.0064 ,0122.0128 ,0268.0430 ..DWIL.0482 .0477 0358 -aus.0228 _nnto.nn97 .0050 _.0.f02Affla o Per. - Per.Ord. .0006.0034.0038 ..22.121.0044 .0220.0100 aie.0232 .0440.0732* ...4.3A2,0522 .0136.0262 .0108.0044 _auk.0962.0074 .0002.0012 Interval OrdinalSample A Percentile Descriptions of Samples Interval 50.084OrdinalSample B Percentile 50.021 MeansMeanSD of of ofMeans MeansSDs 50.009 0.7323.868 50.044 0.7343.900 50.047 4.7110.884 50.012 1.4587.681 1.4357.585 0.8774.689 MeanSD of ofSDs Skews 1.2280.842 0.7220.600 0.0020.400 -1.229 0.5781.661 -1.157 0.5781.540 -0.014 0.2640.407 MeanSDSD of of Skews Kurtosis 2.4281.5190.585 -0.056 1.5880.460 -1.131 0.2640.275 2.4031.490 2.3391.073 -1.118 0.259 OBTAINED PERCENTAGES OF t VALUES FORPositive GIVEN Skewed (N = 5 ) and Negative Skewed(N =15) DISTRIBUTIONS TABLE _1_7_104 LEVELS OF SIGNIFICANCE FOR Int. - Int. A Scales .0067.0010 .0174.0050 .0100..0284 .0906.0250 Levels of Significance .0500 ru1,4* .0500 .0250 .0060.0100 .0028.0050 .0002.0010 Int. - Per.Ord. .noo7.0020 .0080.0008 .0010.0144 .0022*.0324 A-1617rin50 .0076*.0426 Alfa.0014*_0910 .0008.0068 .0034.0002 .0000.0000 Ord. - Ord.Int. .0062.0014 .0084.0170 .0148.0264 .0458*.0326 .0580.0758* .0404.0450 .0198 .0086.0080 .0038.0036 .0004.0002 Ord.Per. - -Per. Int. .0584*.0002 .0880*.0008 .1048*.0010 .1406*.0020* ..1282*.0056* .0076*.1822* ....Q36.1444*.0016* .1088*.0008 .0004.0914* .0574*.0000 Per. - Per.Ord. .0006 0584* .0878*0032 .1048*.0070 .0194.1398* .0418.1776* .0546.1836* .1460*.0318 .1096*.0136 .0070.0922* .0010.0578* Interval OrdinalSample A Percentile Descriptions of Samples Interval OrdinalSample49.937 B Percentile49.498 MeanSDMeans of of Meansof SDs Means 50.0071.7983.173 50.050 3.3251.795 12.92650.37324.739 50.000 3.7141.022 3.7531.017 27.586 7.416 MeanSD of SDsSkews 0.4151.646 0.2941.294 -0.016 6.923 -0.982 0.6011.115 -0.614 0.7960.482 0.3840.0153.500 SDMean of ofKurtosisSkews Kurtosis -0.915 0.6050.606 -0.993 0.6091.159 -1.110 0.5970.530 0.5101.719 -0.404 1.151 -1.073 0.430 TABLE B - 105 OBTAINED PERCENTAGES OF t VALUES Positive Skewed (N =5 ) and Negative Skewed(N =15) FOR GIVEN LEVELS OF SIGNIFICANCE DISTRIBUTIONS FOR Int. - Int. A Scales B .0074.0010 .0050 .0100 .0250 Levels of Significance .0500 .0500.0340 __a=.0250 .0100.005(1 .0050.0024 .0010.0004 Int. - Per.Ord. .0000.0034 Alla.0004.0094 -Dane.0004.0180 .0030*.0360 ABM*.0664.0098* .0142*.0394 .0048*.0162 .0022.0058 .0006.0034 .0000.0002 Ord. - Int.Ord. .0036.0076 .0204* ,glak.0304* .0364.0520* .0640.0822* .0440.0374 .0214.0188 10.0.0064 .0038.0036 .0008.0002 Ord.Per. - -Per Int. .0320*.0000 A=.0004 .0726*.00 .0026* Aug':.1406* .1322*.0140* .0952*.0054* .0020.0606* Ala*.0008 .0000.0242* Per. - Ord.Per. .0274*.0006 ANA,Aule.0068 Aug.0696* Ane.0242aae ,110,,0482 .0522 .0968*.0268 .0132.0432* ,9472.0078 .0022 0242* Interval OrdinalSample A Percentile Descriptions of Samples Interval49.987 OrdinalSample49.925 B Percentile 49.801 MeanSDMeans of ofMeansof SDs Means 49.952 3.1671.766 49.989 1.7693.324 49.974 8.2934.282 3.7181.033 3.7531.018 9.1972.458 MeanSD of ofSDs Skews 0.4381.622 0.3141.282 0.0102.320 -0.9810.5971.106 -0.613 0.4860.786 0.3820.0141.161 MeanSD of KurtosisSkews -0.917 0.5880.597 -1.004 1.0260.596 -1.114 0.5240.591 1.6960.502 -0.400 1.143 -1.067 0.421 TABLE B - 106 OBTAINED PERCENTAGES OF t VALUESPngiriup FOR GIVEN skpwpd LEVELS OF (N = S ) andNeRative Skewed(N =15 Levels of Significance SIGNIFICANCE) FORDISTRIBUTIONS Int. - Int. A Scales B .0090.0010 .0050 .0310*.0100 .0554*.0250 ,A1177*.0500 .0500 0314 -D144.0250 .0100 aaraL .00500014 ADM.0010 Int. - Per.Ord. .0042 ...Qui.0024toll" 410.260.0188 .0150.0368 .03fle.a5456. .0318.0350 .0120.0162 .0050 casz .0008.0016 Anna Ord. - Int.Ord. .0044.0090l= .0132.0190 .0184.0296* .0514*.0364 .0648.0818* .0386.0342 .0182.0152 ,0046.0052 .0020 .0002.0000.moo, Per.Ord. - -Int. Per. .0110.0004 .0222.0034 .0072.0342* .0588*.0156 .0904*.0322 .0328.0588 .0154.0296 .0042.0128 .0062.0018 A000.0012 Per. - Per.Ord. .0014.0072 .0172.0062 .0120.0248 ,0757.0484* .0500.0766* ,0646.0490 .0244.0326 .0106.0130 :0042.0068 A008.0004 Interval OrdinalSample A Percentile Descriptions of Samples Interval50.027 49.970OrdinalSample B Percentile49.960 MeanMeansSD of of MeansSDs Means 49.973 1.7633.192 50.006 3.3391.755 50.0054.1552.124 3.7071.042 3.7461.026 4.5961.233 MeanSD of ofSDs Skews 0.4331.641 0.3151.296 0.0081.155 -0.994 0.5991.116 -0.629 0.4830.794 -0.001 0.3830.577 SDMean of ofKurtosisSkews Kurtosis -0.923 0.5850.594 -1.009 0.5980.870 -1.118 0.5230.589 0.5361.736 -0.378 1.163 -1.069 0.423 OBTAINED PERCENTAGES OF t VALUES FOR TABLE B - 107 GIVEN LEVELS OF SIGNIFICANCE FOR Scales Positive Skewed ON =15 ) andNeeative Skewed(N =30) Levels of Significance .0500 .0250DISTRIBUTIONS .0050 .0010 Int. - Int. A B .0058.0010 .0172.0050 ,0242.0100 .0488*.0250 ,0790,.0500 ,11226,.0372 .0124.0156 .0100.004Q.0056 .0018.0024 .0004.0000 Int. - Per.Ord. ,09113.0002 .0024.0110 .0056.0172 .0176.0346 .0380.0610 .0348.0324 Ala.0132 .0054EM .0022 0022 .0006.0000 Ord. - Ord.Int. .0022.0036 .0150.0088 .0152.0214 .0302.0422 .0550.0706* .0424 .0186 .0062.0066 .0038.0024 .0006.0008 to Ord. - Per. .0004 .0142.0032 .0220.0060 .0418.0176 .0714*.0334 .0526.0390 .0166.0256 .0108 .0062 .0016 Per.Per. - Int.-Ord. Per. .0022.0038.0012 .0042.0104 .0170.0080 .0210.0332 .0588.0412 .0540.0616 .0238.0310 .0106.0138 .0078.0064 .0018.0012 Interval OrdinalSample A Percentile Descriptions of Samples Interval OrdinalSample49.941 B Percentile MeanMeansSD of of MeansSDs Means 50.000 3.7131.028 50.034 3.7851.024 50.039 4.6021.230 50.004 0.7183.859 0.7073.865 0.923 0.8514.704 MeanSD of SDsSkews 0.9811.119 0.6200.801 0.0090.586 -1.222 0.8370.586 -0.719 0.5870.456 0.2610.0120.395 MeanSDSD of of Skews Kurtosis 0.4980.6031.740 -0.397 0.4861.180 -1.070 0.3790.428 1.4972.473 -0.075 1.612 -1.151 0.250 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF TABLE SIGNIFICANCE FOR Scales .0010 Positive Skewed .0050 .0100 (N = 5) and Negative Skewed(N =15) DISTRIBUTIONS .0250 Levels of Significance .0500 .0500 .0250 .0100 .0050 .0010 Int. - Int. A B _0014 _00t32.0042 .0052.0064 ...013z.0178 .0392.0300 .0004*.0006* .0000* .0000 _oosa .0000 Int.Int. - -Per. Ord. ulnannl4 .0030.0006 .0052.0014 .0130.0046* .0132*.0294* .0008*.0028* .0000*.0006* .0002.0000 ,ffliaQM .0000 Ord. - Int.Ord. mu.0014 .0006.0036 .0014.0060 .0046*.0164 .0122*.0370 .0024*.0004* .0000*.0008* .0000.0002 .0000mpg .0000.0000 to Per.Ord. - Int.Per. -12000.0102 .0240 .0386* .0708* .1000* .0830* .0482* .0258 -OM.0166 .0050 ocoI-. t Per. - Per.Ord. .0016.0174 .0060.0376* .0098.0538* .0286.0880* .0596.1224* .0312.0898* .0140.0572* .0316*.0042 .00200226 .0004 Interval OrdinalSample A Percentile Descriptions of Samples Interval 51.274OrdinalSample B Percentile52.813 MeanSDMeans of of Meansof SDs Means 50.022 3.2291.825 50.049 3.3721.799 24.95712.76550.240 50.08418.397 5.208 15.294 4.237 28.909 7.911 MeanSD of ofSDs Skews 0.4321.693 0.3091.333 0.0056.862 -1.003 0.5985.482 -0.821 0.5083.451 -0.047 0.3923.624 SDMean of ofKurtosisSkews Kurtosis -0.922 0.5770.596 -0.996 0.9330.607 -1.116 0.5220.591 1.722 0.546 0.0891.283 -1.072 0.436 TABLE B - 109 OBTAINED PERCENTAGES OF t PeL.itive Skewed (N = a..) andNegstwd Skewep(N i=1) VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR DISTRIBUTIONS A Scales B .0010 /MO .0100 ..32f.0 Levels .0500 of Significance .0500 .0250 .0100 .0050 .0010 Int. - Ord.Int. .0024 ._.:064 .0124 _,J.L, .0434 .0066*.0020* .0016* 4WD000D MODMOLL ..1112.411.moo_ Int. - Per. -alaa .0002 ...g49.1 .0064 Am _.1172 .004Q*o::: ..11418&LIE* A074*.01 6* ,ac..5.2.4*_Aarmin* Arm.nn16 0004 MOLLamca. Ord. - Int.Ord. .0022 A070 Alift .0106 .1122 .0404 .0076* .nni,* .onnn MOO .2000_ G' Ord. - Per. .0002z0220 .000? ,220 _MAO.0568* .0884*.0116* Ala*.0594 _jr,::12Apt2* MO.0150 .0004 .0000 0012 t-A 1 Per. - Int. .0106 .0234 .0356*.e.;52* 05 O.* .0900* :,20$ .0356 .0144 ,00E8,0056 .0012 o..0 Per.Per. - -Ord. Per. .0008.0100 ...2(.6§...11720 &in _2.0266 .053Z .0488 .0252 ,0100 .0066 .0016 Interval OrdinalSample A Perc.aZ..i.le Descriptions of Samples Interval OrdinalSample50.055 B Percentile 49.998 MemMeansSD ofof of SDsMeans Means 49.939 1.7803.156 49.977 1.7833.325 4.9.931 8.2844.301 49.979 7.4072.074 7.340 2.040 2.4529.155 MeanSD of ofSDs Skews 0.4241.626 0.3131.290 2.3270.006 -0.991 2.2490.609 -0.953 2.1000.605 -0.011 0.3851.190 -4DMean ofSD Skewsof Kurtosis -0.916 0.6040.596 -0.997 0.6031.383 -1.112 0.5260.597 1.7420.528 0.2071.728 -1.043 0.427 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN TABLE B - 110 LEVELS OF SIGNIFICANCE FOR Scales B .0010 Positive Skewed (N =5 .0050 .0100 .0250 ) andNegative Skewed(N =15 Levels of Significance .0500 .0500 ) DISTRIBUTIONS.0250 .0100 .0050 .0010 Int. - Int. A .0014.0016 .0040.0046 .0082 .0208.0226 .0424 .0076*.0068* AMR*.0038* ..0012.0012 .0006 Affla Ord.Int. - -Int. Ord.Per. .0016.000a .0050.0012 .0074.0028 .0226.0096 .04120220,422 .0070*.0342 .0030*.0164 .0008.0066 .0004.0030.0006 ...QOMAIM.1218. Ord. - Per.Ord. .0016.0004 .0018.0040 .0072.0034 .0098.0208 ...Alga.09gg* .0372.0072* .0182.0028* .0062.0010 .0034.0004 .0016.0000 i-= Per.Per. - -Int. Ord. .0016.0012 .0064.0056 _Mak.0082, .0234.0249 .0472.0470 .0096*.0106* ,0038*J1(13$' .00tn .0004 .0000 o Per. - Per. ,nagii .0042 Sample A .0078 .0210 Descriptions of Samples .0460 .0580 .0288 Sample B AWL.0106 .0052 Ana, SDMeans of Meansof Means Interval49.978 1.760 50.018Ordinal1.765 Percentile 50.031 2.131 Interval49.943 2.111 50.019Ordinal2.081 Percentile 49.975 1.255 MeanMeanSD of ofSDs Skews 0.4391.5723.168 0.3151.2333.324 0.0111.1334.142 -0.987 2.2437.414 -0.951 2.0997.347 -0.002 0.5914.574 SDMean of ofKurtosisSkews Kurtosis -0.907 0.5880.603 -0.999 0.9440.607 -1.108 0.5250.596 0.5170.6081.743 1.7290.2030.607 -1.034 0.4430.387 111 OBTAINED PERCENTAGES OF t VALUESPositive Skewed (N =15 ) andNegative Skewed(N TABLE B - FOR GIVEN LEVELS OF SIGNIFICANCE =30) DISTRIBUTIONS FOR A Scales B .0010 .0050 .0100 .0250.n7A6 Levels of Significance .0500.0514 .0500Ainco* .0250_0020* .0100Ann', .0050_moo .0010.000Q Int.Int. - -Int. Ord. .00200026 .0068.0070 _fills.0086.0136 .0236.0298 .0460.0530 .0090*.0322 .0018*.0136 .0002.0042 .0014.0000 .0000 Ord.Int. - Int.Per.Ord. .0016.0004.0014 ,0036.0068.0066 .0118.0120 .0274.0280 .0498.0474 .0086*.0092* .0024*.0020* .0000.0002 .0000.0000 .0000.0000 Per.Ord. - Int.Per. .0004.0018 .0028.0076 .0136.0072 .0286.0228 .0434.0532 .0122*.0362 .0152 A0112.0050 .0024.0000 .0000.0000 1 Per. - Ord.Per. .0016.0008 .0084 0050, .0118.0136 .0286.11228 ,0542 .0116, -0130*.0474 Alia*.0040*.0226 .0004.0006 .0000.0046 AQQQ .0010 Interval OrdinalSample A Percentile 50.005 Descriptions of amples Interval 50.019 OrdinalSample50.097 B Percentile 50.021 MeansMeanSD of ofof Means MeansSDs 49.979 3.7131.025 50.011 3.7881.026 4.6201.233 1.4587.672 7.5711.428 0.8684.682 MeanSD of ofSDs Skews 1.1120.987 0.7990.623 0.5820.015 -1.232 0.5731.678 -1.161 0.5711.560 -0.012 0.4010.265 MeanSDSD of of Skews Kurtosis 1.7460.5120.603 -0.397 1.1780.486 -1.076 0.3820.421 2.3791.501 2.3041.080 -1.110 0.254 OBTAINED PERCENTAGES OF t VALUESPositive FOR Skewed LIVEN LEVELS OF SIGNIFICANCE (N = 15) andmeRative Skewed(N = 5 TABLE R - 112 ) DISTRIBUTIONS FOR Int. - Int. A Scales B .1018*.0010 .1530*.0050 .1802*.0100 .2230*.0250 Levels of Significance .2648*.0500 .0500.1286* .0866*.0250 .0100.0514* .0356*.0050 .0142.0010 Int. - Per.Ord. .0796*.1018* .1166*.1560* .1870*.1410* .1874*.2368* .2357*.2784* .1444*.1050* .1124*.0672* .0870*.0410* .0702*.0288* .0438*.0132 Ord. - Ord.Int. .0988*.1006* .1526*.1516* .1774*.1860* .2340*.2256* a702*.2632* .1046*.1294* .0674*.0868* .0422*.0514* .0306*.0356* .0134.0148 oa Per.Ord. - Per.Int. .0000.0798* .0012.1154* ,0024.1410* A918.1880* .0190*.2352* .0264*.1454* 0092.1114* .0030.0864* .0010.0700* .0444*.0002 1-. Per. - Per.Ord. .0020.0000 .0014.0088 .0184.0030 .0384.0064 .0774*.0188* .0418.0140* .0196.0054* .0092.0014 .0006.0036 .0000.0008 Interval OrdinalSample A Percentile Descriptions of Samples Interval49.957 51.119OrdinalSample B Percentile 52.559 MeanMeansSD of of Means SDsMeans 50.015 3.7251.041 50.048 1.0343.796 27.67650.319 7.391 15.790 9.125 13.410 7.407 25.97313.739 MeanSD of SDsSkews 0.9811.133 0.8160.615 0.0033.515 -0.436 8.175 -0.384 0.5975.693 -0.031 0.5987.221 MeanSD of KurtosisSkews 1.7360.5110.605 -0.393 1.1820.493 -1.066 0.3860.432 -0.930 0.5910.575 -0.951 0.568 -1.118 0.525 TABLE B - 113 OBTAINED PERCENTAGES OF t VALUES PositiveFOR GIVEN Skewed LEVELS OF SIGNIFICANCE FOR (N = 15 ) and Negative Skewed(N 5) DISTRIBUTIONS A Scales B .0010 .0050 .0100 .0250 Levels of Significance .0500 .0500 .0250 .0100 .0050.0134 .0010.0046 Int. - Int.Per.Ord. .0338*.0368*.0316* .0580*.0708*.0690w .0748*.0904*.0940* .1140*.1334*.1324* .1532*Lae.17Rn* -9E60*.1342*.0842* .0916*.0512*4528* .0628*.0242.0248 .0474*.0150 .0238*.0060 Ord.Ord. - -Ord. Int. .0236*.0192 .0538*.0562* .0766*.0784* .1230*.1208* .1706*.1682* .0872*.0876* ,2522*.0516* .0248 .0144.0142 .0054.0040 to . Ord. - Per. .0002.0270* .0018.0528* .0042.0714* .0110.1062* .0270*.1508* .0334.1376* .0148.0938* .0050.0640* .0022.0472* .0002.0238* 1-. Per. - Ord.Int. .0002 .0020 .0040 .0108 .0284* .0306* .0130 .0052 .0020 .0002 Per. - Per. ,0004 ,0042 Sample A .0086 .0240 Descriptions of Samples .0470 .0516 .0234 Sample B .0108 .0054 .0014 SDMeans of Meansof Means Interval50.000 1.038 50.032Ordinal 1.033 Percentile 50.072 2.486 Interval50.030 3.665 Ordinal50.120 3.588 Percentile 50.106 4.328 MeanMeanSD of ofSDsSDs Skews 0.9821.1153.715 0.6170.8023.785 0.0071.1659.217 -0.442 3.3456.356 -0.521 3.1206.316 -0.018 2.3248.228 SDMean of ofKurtosisSkews Kurtosis 1.7170.5120.607 -0.396 1.1400.486 -1.064 0.3910.433 -0.922 0.5750.593 -0.306 0.617 .480 -1.108 0.5160.591 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE TABLE 4 - 114 FOR Scales B .0010 Positive Skewed .0050 .0100 (N =15 ) andNeeative Skewed(N =5 .0250 Levels of Significance .0500 .0500 ) DISTRIBUTIONS.0250 .0100 .0050 .0010 Int. - Int. A .0336* .ni1,4* .1224* _1717* _OR47* n416* .0250 .0124 1 -LICISE Int. - Ord. .0104.0366* ohne.0274*_0690* .0376*.0830* .0590*.1228* .0900*lfga* _nue nfica ,0356.0502* .0166.0242 _min.0090 _0056 Ord.Int. - -Ord.Int. Per. ,Q252!.0282* .0520*.0482* .0740*.0698* .1150*.1134* .1578*.1596* .0846*.0856* .0510*.0520* .0258 .0172.0180 _nafin_Lam.0056 ed Ord. - Per. .0060 .0174 .0280 .0488* .0798* .0636 .0368 .0182 .0142.0088 .0024 1 Per. - Ord.Int. .0076.0070 .0224.0266* A402,.0386* .0770*.0714* .1184*.1230* .0750*.0768* .0432.0462* .0220.0210 .0152 .0040.003k Per. - Per. .0012 .0060 Sample A .0102 .0268 Descriptions of Samples .0506 .0524 .0288 Sample B .0128 .0060 .0016 MeansSD of of Means Means Interval 50.027 1.042 Ordinal50.058 1.033 Percentile 50.067 1.233 Interval49.947 3.630 Ordinal50.035 3.556 Percentile 50.004 2.169 MeanSD of SDsSkewsSDs 0.9831.1233.731 0.6140.8103.794 0.5944.6100.002 -0.445 6.4183.266 -0.511 6.3623.046 -0.010 1.1634.139 SDMean of ofKurtosisSkews Kurtosis 0.5971.7350.500 -0.405 1.1800.482 -1.078 0.4180.372 -0.920 0.5780.594 -1.226 0.622 .661 -1.105 0.5200.592 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR TABLE B - 115 A Scales B .0010 Positive Skewed .0050 .0100 (N =30 ) andNegative Skewed(N =15) DISTRIBUTIONS .0250 Levels of Significance .0500 .0500 .0250 .0100 .0050 .6010 Int. - Ord.Int. .0184.0200 .0380*.0406* .0534*.0550* .0890*.0870* .1308*.1304* .0582.0602 .0300.0318 .0130.0122 .0058.0064 .0016.0012 Int. - Per. .0026 .0128 : .0222 .0422 .0694* .0492 .025Q .0098 .0048 .0008 Ord. - Ord.Int. A160.0150 .0360*.0340* .0512*.0500* .0822* .1230*.1206* .0630.0622 .0322.0332 .0144.0146 .0070.0066 .0012.0016 Ord. - Per. .0076.0016 .0216.0104 .0352*.0176 .0642*.0330 .1034*.0620 .0602.0564 .0324.0276 .0142.0122 .0058.0066 .0006.0008 1-. Per.Per. - -Ord. Int. .0072 .0218 .0358* .0652* .1024* 0588 .0314 .0138 .0066 .0012 to Per. - Per. .0006 ,OPM Sample A .0086 .0240 Descriptions of Samples .0450 .0526 .0250 Sample B .0126 .0064 .0006 MeansSD of of Means Means Interval49.989 0.731 50.022Ordinal 0.727 Percentile 50.024 0.877 Interval50.000 2.055 50.066Ordinal 2.025 Percentile50.005 1.219 MeanSD of ofSDs SkewsSDs 0.8271.2343.852 0.5840.7243.886 4.7050.0090.401 -0.995 2.2277.391 -0.956 2.1067.331 -0.005 0.5894.577 MeanSDSD of of Skews Kurtosis 0.5802.4101.536 -0.066 1.5350.448 -1.134 0.2600.268 1.7490.5400.606 1.7310.2110.601 -1.042 0.4370.377 TABLE B - 116 OBTAINED PERCENTAGES OF t VALUESPositive Skewed (N = 5 ) and FOR LeptokurticGIVEN LEVELS OF SIGNIFICANCE (N ) DISTRIBUTIONS FOR A Scales B .0010 .0050 .0100 .0250 Levels of Significance .0500 .0270*.0500 .0094.0250 .0032.0100 .0014.0050 .0010.0002 Int.Int. - -Int. Per.Ord. .0052.0038 .0120.0134 ,01212..0214 .0410.0404 0442* 025.6A734,.0672 .0750*.0378 A48*.0150 .0364*.0052 .0250*.0024 .0006.0148 Ord.Ord. - -Int. Ord. .0032.0032 .0098.0106 Auum.0166Ma* iscal.0344 .0600.0656 .0432.0374 .0198.0146 .0070.0062 .0040.0048 .0010.0008 to Ord. - Per. .0086.0110 .0212.0186 .0300*.0262 .0462*.0444* .0680.0724* .0718*.0758* .0496*.0556* .0318*.0362* .0222.0252* .0110.0148 Per. - Per.Int.Ord. .0026.0084 .0080.0188 .0254.0124 .0458*.0274 .0718*.0512 .0738*.0566 .0496*.0314 .0146.0322* .0084.0222 .0030.0108 Interval OrdinalSample A Percentile Descriptions of Samples Interval 49.952OrdinalSample B Percentile 49.789 MeanMeansSD of of MeansSDs Means 50.005 3.2011.809 50.035 3.3451.802 12.96450.19724.884 50.003 3.7242.228 2.1933.942 27.64814.257 MeanSD of of-SkewsSDs 0.4371.646 0.3171.293 0.0077.010 -0.002 0.7712.452 -0.008 0.6821.874 0.6500.0027.163 MeanSD of KurtosisSkews -0.915 0.6000.603 -0.991 0.6021.303 -1.116 0.5930.522 -0.892 0.673 -1.027 0.845 -1.137 0.586 TABLE B - 117 OBTAINED PERCENTAGES OF t PositiveVALUES FOR Skewed GIVEN LEVELS OF SIGNIFICANCE (N = 5 ) and Leptokurtic (N = 5 ) DISTRIBUTIONS FOR Int. - Int. A Scales B .008u.0010 .0174.0050 ,Q232..0100 .0354.0250 Levels of Significance .0578.0500 .0500.0512 .0334.0250 .0204.0100 .0152.0050 .0070.0010 Int.Int. - -Per. Ord. .nloo.0110 .0212.0220 .0294*.0270 .0470*.0194 .0592.0684 .0692*.0590 .0376.0486* ,0268.0122* .0212.0240 .012298 Ord. - Int.Ord. .0072 ...41231..0164 .0258.0226 .0390.0348 .0582.0568 .0600.0528 .0384.0140 .0262.0208 .0208.0152 Aldaa.0090 Ord. - Per. .0026.0100 0222 .0296* .0460* .0524.0682 .0502.0698* .0274. 0488* .0322*.0134 .0092.0240 .0030.0122 1-. t Per. - Int.Ord. ,0016.0014 .0082 .0146.0152 .0296.0280 .0528 .0552 .0286 .0146 .0100 .0032 --,1- Per. - Per. .0020 .0060 Sample A .01G8 .0236 Descriptions of Samples .0494 .0528 .0260 Sample B .0146 .0068 .0026 SDMeans of Meansof Means Interval49.984 1.782 50.017Ordinal 1.781 Percentile 50.10812.819 Interval11.24750.280 49.88COrdinal 8.029 Percentile 15.27249.937 MeanSD of ofSDs SkewsSDs 0.4341.6243.191 0.3081.2793.339 -0.00024.933 6.995 12.31818.742 0.003 -0.01315.059 5.642 29.798 0.0057.737 SDMeanSD of of Kurtosis SkewsKurtosis -0.897 0.6160.603 -0.986 0.6061.286 -1.1050.6020.529 -0.919 0.7550.621 -1.048 0.6660.585 -1.147 0.5910.627 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE TABLE B - 118 FOR Scales B .0010 Positive Skewed (N = 15) and .0050 .0100 .0250 Levels of SignificanceLeptokurtic.0500 .0500 (N =15 ) DISTRIBUTIONS.0250 .0100 .0050 .0010 Int. - Int.Ord. A .0022.0024 .0064.0082 .0146.0160 .0392.0376 .0724*.0662 .0412.0362 .0166.0136 .0044.0038 .0018.0022 .0000 Ord.Int. - -Int. Per. .0020.0040 .0050.0102 .0132.0154 A298.0320 .0606.0564 .0424.0554 j186.0290 .0056.0142 .0022.0080 .0002.0024 Ord.Ord. - -Ord. Per. .0038.0016 .0100.0050 .0112.0160 .0300.0320 .0566.0584 .0562.0480 .0290.0196 .0146.0074 .0080.0028. .0026.0000 to 1 Per. - Int. .0030 .0088 .0142 .0296 .0572 .0560 .0320 .0166 .0092 .0024 co Per.Per. - Ord.- Per. .0010.0030 .0042.0090 .0142.0094 .0262.0292 .0516.0532 .0492.0558 .0320.0252 .0170.0108 .0090.0062 .0024.0006 Means of Means Interval49.984 50.016OrdinalSample A Percentile 50.114 Descriptions of Samples Interval50.018 49.967OrdinalSample B Percentile 49.816 MeanSD of SDsMeans 1.1063.7021.034 0.7961.0293.775 27.639 3.5357.397 4.4011.2851.899 4.4871.3611.256 30.680 3.3588.250 MeanSD of SkewsSkews 0.6000.984 0.4840.619 -1.064 0.3810.011 0.0031.1201.212 -0.138 0.8320.005 -1.259 0.4240.013 SDMean of ofKurtosis Kurtosis 1.7200.510 -0.397 1.164 0.426 2.310 1.727 . 0.418 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN TABLE _El 7_119 LEVELS OF SIGNIFICANCE FOR A Scales B .0010 Positive Skewed .0050 .0100 (N =15 ) and Leptokurtic .0250 Levels of Significance .0500 .0500 (N = 15 ) DISTRIBUTIONS .0250 .0100 .0050 .0010 Int. - Int.Ord. ...028.0016 .0072.0048 .0092.0136 .0268.0218 .0482.0534 .0548.0468 .0283,.0206 .0084,.0122 ...0118..0064 .00180.025. Ord.Int. - -Int. Per. .401 .0050.0100 ,01116.0090 .0214.0300 .0546.0482 .0478.0580 .0334.0216 .0144,.0084 ,0094,.0042 .0032.0006 Ord. - Per.Ord. -110213. nnin004, .0100.0070 .0134.0140 .0268.0298 .0538.0522 .0584.0552 .0324.0284 .0120.0140 .0088.0064 .0016.0032 Per. - Ord.Int. ,0008.0014 .0050.0038 .0094.0074 .0206.0196 .0398.0428 .0532.0496 .0280.0232 .0116.0094 .0056.0040 .0014.0012 . .0098 .0050 .0008 Per. - Per. 10012 Interval .0050 OrdinalSample A .0088 Percentile.0212 Descriptions of Samples .0432 .0532 Interval .0278 OrdinalSample B Percentile . 49.845 49.816 MeanMeansSD of of MeansSDs Means 50.011 1.0173.721 30.046 3.7941.008 50.32227.735 7.243 49.91921.9826.285 17.0114.645 33.0808.942 MeanSD of ofSDs Skews 0.9751.110 0.6070.801 -0.002 3.520 -0.009 9.0971.178 -0.002 0.6223.530 0.4070.0183.609 MeanSD of KurtosisSkews 0.5010.6081.757 -0.415 0.4841.177 -1.0810.3740.414 2.2441.038 -0.450 0.987 -1.237 0.406 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE TABLE g - 120 FOR A Scales B .0010 Positive Skewed (N = 5 ) and Leptokurtic .0050 .0100 .0250 Levels of Significance .0500 .0500 (N =15 ) .0250 DISTRIBUTIONS .0100 .0050 .0010 Int. - Ord.Int. .0006,.0902 .0034.0054 .0098.0058 .0170.0264 .0492.0380 .0358.0378 .0176.0196 .0074.0096 .nn4R n0l9 .0006.0002 Ord.Int. - -Int. Per. .0002.0012 .0050.0006 =0012.0120 .0286.0030* .0496.0068* .0420.0086* .0218.0042* .0118.0018 .0058.0n19, .0014.0002 Ord. - Per.Ord. .0002 .0006.0030 .0012.0076 .0030*.0172 .0070*.0404 .0084*.0400 .0044*.0210 .0018.0090 .0032.0012 .0002.0010 Per.Per. - -Ord. Int. .0526*.0522* .0864*.0858* .1048*.1050* .1380*.1410* .1748*.1762* .1738*.1728* .1368*.1362* .1026*.1038* 024*.0824* .0550*.0542* ts) Per. - Per. .0006 .0032 Sample A .0068 .0192 Descriptions *r7 Samples .0390 .0480 .0222 Sample B .0094 .0040 .0010 MeansSD of of Means Means Interval49.957 1.770 49.991Ordinal 1.761 Percentile 49.94912.722 Interval 49.979 1.266 Ordinal49.920 1.249 Percentile49.498 8.258 MeanSD of SDsSkewsSDs 0.4411.6243.171 0.3181.2763.325 24.855 0.0156.863 -0.002 1.8614.365 0.0004.4691.371 30.554 0.0253.379 MeanSD of KurtosisSkews -0.918 0.5920.591 -1.023 0.9100.592 -1.123 0.5220.586 2.2991.0961.198 -0.128 0.8371.754 -1.248 0.4550.423 TABLE R - 121 OBTAINED PERCENTAGES OF t VALUES FOR GIVENPositive LEVELS SkewedOF (N = 5 ) and leptokurtic (N =15 ) SIGNIFICANCE DISTRIBUTIONS FOR Int. - Int. A Scales B .0002.0010 .0004.0050 .0010.0100 .0016*.0250 Levels of Significance .0034*.0500 .0054*.0500 .0016*.0250 .0006.0100 .0006.0050 ,00Q2.0010 Int. --,Ord. Per. .0004.0002 .0008.0004 .0012 .0024*.0018* .0046*.0044* .0076* .0030*.0022* .0012.0006 .0004.0004 ,0004.0002 . Ord. - Int. .0002 .0004 .0010 .0016* .0034* .0048* .0016* .0004 .0002 Ord.Ord. - -Ord. Per. .0004.0002 .0008.0004 .0012.0010 .0018*.0024* .0046*.0046* .0072* .0024*.0032* .0010.0008 .0004 201.0002 m I Per. - Int. .0060 .0186 ,0278 .0494* .0748* .0754* .0476* .0238* .0170 .0074 naI-.1-. Per. - Per.Ord. .0082.0000 .0230.0028 .0052.0368* .0138.0616* .0980*.0332 .0376.1000* .0622*.0158 .0062.0346* .0034.0226 .0004.0092 tv .4, h Interval OrdinalSample A Percentile Descriptions of Samples Interval OrdinalSample49.822 B Percentile 49.681 MeanSDMeans of ofMeansof SDs Means 49.981 3.2021.789 50.012 1.7823.359 12.83150.00425.080 22.19450.009 6.300 17.111 4.644 33.1408.890 MeanSD of SDsSkews 0.4291.632 0.3051.284 -0.000 0.5886 . 867 9.28391.1850.014 0.6330.0083.550 0.4070.0253.716 MeanSD of KurtosisSkews -0.931 0.5830.589 -1.012 0.5971.319 -1.124 0.522 1.0532.236 -0.429 0.998 -1.237 0.414 OBTAINED PERCENTAGES OF t VALUES FOR GIVENPositive LEVELS Skewed OF SIGNIFICANCE (N = 15) and FOR Leptokurtic TABLE B -122 (N = 5 ) DISTRIBUTIONS Int. - Int. A Scales B .0416*.0010 .0726*.0050 0954*.0100 .1344*.0250 Levels of Significance .1826*.0500 .1774*.0500 _17144*.0250 .0870*.0100 .0656*.0050 .0364*.0010 Int. - Per.Ord. .0622*ale ,0852*.0706* .0932*.1052* .1440*.1306* .1802*.1700* .1886*.1828* .1312*.1478* .0924*.1118* .0924*.0736* .0656*.0416* Ord. - Int.Ord. Alme.0396* .0684*.0698* .0886*.0928* .1294*.1342* .1820*.1696* .1846*.1810* .1328*.1294* .0930*.0872* .0746*.0668* .0350*.0416* to Ord. - Per. .0626* .0848* .1050* .1426* .1788* .1902* .1490* .1122* .0924* .0662* I-, t Per.Per. - -Int. Ord. .0000..0000 .0008.0016 .0046.0018 .0072.0122 .0202*.0294* .0198*.0268* .0104.0084 .0026.0032 0014.0016 .0004.0004 IV Per. - Per. .0024 .0102 Sample A .0168 .0370 Descriptions of Samples .0630 .0722* .0424 Sample B .0166 .0098 .0024 SDMeans of Meansof Means Interval49.993 1.037 50.031Ordinal 1.039 Percentile 50.238 7.510 Interval10.67750.054 49.762Ordinal 8.076 Percentile 49.63515.364 MeanSD of SDsSkews 0.9751.1093.694 0.6100.7983.775 -0.00127.627 3.475 11.71318.374 0.010 15.078-0.001 5.718 29.774 0.0147.753 MeanSD of KurtosisSkews 1.7370.5060.608 -0.402 0.4891.157 -1.067 0.4210.388 -0.941 0.6110.740 -1.059 0.6620.582 41.595-1.740 0.634 OBTAINED PERCENTAGES OF t VALUESNegative FOR GIVEN Skewed LEVELS OF SIGNIFICANCE FOR (N = 5 ) and Leptokurtic TABLE B - 123 (N = 5 ) DISTRIBUTIONS ;int. - Int. A Scales B .0006.0010 .0050 .nni6.0100 .0250 Levels of Significance .0308.0500 .0742*.0500 .0414.0250 .0174.0100 .0090.0050 .0032.0010 Int.Int:_-'- - Per.Ord. .0104.0010 .0220osai.0034 on _0122.0418.0146 .0616.0352 .0720* .0506*.0402 .0354*.0192 .0264*.0102 .0144.0036 Ord.Ord. - -Ord. Int. .0012.0018 .0040.0030 egg..0074.0078 .0202.0180 .0404.0376 .0632.0634 m54.0334 .0144.0132 .0086.0088 .0030.0016 w Per.Ord. - Per.Int. .0118.0106 .0.222..0260* .0332*.0290 .0526*.0422 .0764*.0620 .0634.0720* 41416_.0504* -.0348* .0268 .0196.0265* .0146.0108 t.,4.4I-. Per. - Per.Ord. .00300122 .0086.0246* .0140.0338* .0282.0534* .0522.0766* .0514.0638 .0262.0422 .0110.0264 .0070.0194 .0024.0106 Interval OrdinalSample A Percentile Deperiptions of Samples Interval Ordinal,.9.908Sample B Percentile 49.423 MeanSDMeans of ofMeansof SDs Means 49.980 1.8403.208 49.922 1.8143.320 13.00849.44224.715 49.957 3.6862.174 3.9282.146 27.66914.079 MeanSD of ofSDs Skews -0.443 1.673 -0.320 1.301 -0.006 6.887 0.0062.411 0.0141.895 0.6440.0267.047 MeanSD of SkewsKurtosis -0.919 0.5990.596 -0.955 1.3510.605 -1.114 0.531C.596 -0.9C2 0.6510.763 -1.032 0.6761.534 -1.137 0.582 TABLE B -_124 (-1 OBTAINED PE\CENTAGES OF t VALUES Negative Skewed (N = 5 ) and FOR GIVENLeptokurtic LEVELS (N = 5 OF SIGNIFICANCE ) DISTRIBUTIONS FOR Int. - Int. A Scales B .0058.0010 .0130.0050 .0192.0100 .0136.0250 Levels of Significance .0560.0500 A0566.0500 _0146.0250 .0240.0100 .0178.0050 .0090.0010 Int. - Per.Ord. .0092.0098 .0196.0224 .0310*.0258 .0478*.0382 .0710*.0498 42648.0716* '.0416 .0544* .0100*.0354* .0236 .0156.0124 Ord. - Int. .0088.0054 .0200.0132 .0260.0196 .0394.0348 .0580.0612 .0566.0636 .0412.0352 .0298*.0238 .0224.0170Arm* .0106.0086 Ord.Ord. - -Ord. Per. ..0094 .0222 .0310* .0494* .0710* .0726* .0548* .0352* .0276*.0088 .0154.0024 w t Per. - Int. Ord. .0016.0008 .0090.0072 .0154.0140- .0310.0314 .0586.0572 .0568.0552 .0334.0284 .0164.0150 .0098 .0032 LsIVI-, Per. - Per. - .0018 .0080 Sample A .0136 .0298 Descriptions of Samples .0508 .0514 .0304 Sample B .0164 .0104 .0028 MeansSD of of Means Means Interval50.016 1.816 49.947Ordinal 1.790 Percentile 12.86349.582 Interval10.82649.866 49.882Ordinal 8.112 Percentile49.81215.537 MeanSD of SDsSkews -0.418 1.6693.166 -0.304 1.3053.294 24.651 0.0126.853 -0.01911.76218.381 -0.01215.120 5.781 29.691 0.0007.883 SDMean of ofKurtosisSkews Kurtosis -0.943 0.6110.601 -0.972 1.5760.606 -1.127 0.5250.589 -0.911 0.6130.758 -1.024 0.5900.684 -1.122 0.5800.648 OBTAINED PERCENTAGES OF t VALUES FOR TABLE B - 125 GIVEN LEVELS OF SIGNIFICANCE FOR A Scales B .0010 Negative Skewed .0050 .0100 (N = 15) and Leptokurtic .0250 Levels of Significance .0500 .0500 (N =15) .0250DISTRIBUTIONS .0100 .0050 .0010 Int. - Ord.Int. .0004 ,01126..0010 .0511.0036 .0166.0152 .0372.0374 .0678.0676 .0380.0376 .0170.0164 .0084.0086 .0036.0032 Ord.Int. - Int.Per. .0006.0024 .0020.0086 .0124.0064 .0282.0206 .0490.0506 .0566.0592 .0310.0254 .0104.0152 .0068.0098 .0018.0024 Ord. - Per.Ord. .0024.0006 .0032.0088 .0074.0124 .0290.0200 .0518.0456 .0578.0574 .0302.0302 .0154.0102 .0098.0074 .0028..0024 to Per. - Int.Ord. .0042.0040 .0104.0110 .0182.0180 .0380.0386 .0624.0628 .0502.0500 .0260.0248 .0122.0118 .0070.0072 .0026 1 Per. - Per. .0016 .0064 .0122 .0274 Descriptions of Samples .0560 .0500 .0244 Sample B .0092 .0060 .0020 Means of Means Interval49.989 OrdinalSample49.930 A Percentile 49.481 Interval 50.019 1.276 Ordinal49.967 1.251 Percentile 49.761 8.211 SDMean of ofSDsMeans SDs 1.1103.7311.045 0.7933.7591.039 27.624 7.5293.463 4.3851.885 1.3844.490 30.602 3.334 Mean of Skews -0.991 -0.615 0.014 . 0.0071.225 0.0090.855 0.4260.011 MeanSD of KurtosisSkews 0.5350.5991.732 -0.397 0.4871.167 -1.072 0.4180.387 2.3411.145 -0.090 1.774 -1.250 0.427 OBTAINED PERCENTAGES OF t VALUES FORNegative GIVEN LEVELSSkewed OF(N SIGNIFICANCE= 15) and Leptokurtic FOR TABLE (N = 15) DISTRIBUTIONS Int. - Int. A Scales B .0008.0010 .0048.0050 .0092.0100 .0246.0250 Levels of Significance .0500 .0500.0508 .0236.0250 ...mulL.0100 .0058.0050 .0014.0010 Int. - Per.Ord. .0012 .0082.0062 .0136.0114 .0288.0234 .Sallai88 .0574.0580 .0312.0294 .0150.0154 .0098.0082 .0040.0026 Ord. - Int.Ord. .0012.0008_wog .0064.0050 .0114.0094 .0242.0270 ,25.14.0500 .0534.0496 .0288.0228 .0140.0102 .0078.0052 .0024.0018 Ord. - Per. ,2004.0028 .0048.0080 .0112.0132 .0288.0296 .0530.0522 .0478.0564 .0256.0302 .0110.0148 .0102.0064 ' .0008.0040 N1-.w 1 Per.Per. - -Int. Ord. .0004 .0062 .0090 .0300 .0562 .0530 .0292 .0138 .0080 .0010 T Per. - Per. .0014 .0044 Sample A .0098 .0256 Descriptions of Samples .0496 .0482 .0278 Sample B .0130 .0066 .0020 SDMeans of Meansof Means Interval50.007 1.055 49.945Ordinal 1.041 Percentile 49.612 7.487 Interval50.104 6.360 49.804Ordinal 4.634 Percentile49.723 8.849 MeanSD of ofSDs SkewsSDs -0.981 1.1253.714 -0.614 0.7913.756 27.647 0.0143.487 22.050 0.0249.396 -0.00217.059 3.536 33.0840.0193.632 SDMean of ofSkewsKurtosis Kurtosis 0.5170.6041.731 -0.397 1.1490.487 -1.073 0.4290.391 2.2681.0071.173 -0.433 1.0080.632 -1.241 0.4030.398 TABLE R - 127 OBTAINED PERCENTAGES OF t Negative Skewed (N = 5 VALUES FOR GIVEN) and LEVELSLeptokurtic (N =15 OF SIGNIFICANCE ) DISTRIBUTIONS FOR Int. - Int. A Scales B .0010.0008 .0038.0050 .0062.0100 .0190.0250 Levels of Significance .n169.0500 .0464.0500 .0230.0250 .0102.0100 .0054.0050 .0012.0010 Int.Int. - -Ord. Per. .0000.0006 .0004.0022 .0010.0044 .0Q28*.0144 .0058*.0320 .ol9g_nn64* .0018*.0168 .0006.0058 .0000..0022 .0000.0006 Ord. - Int.Ord. .0010.0018 .0036.0054 A026 .0184,.0206 .0370.0420 .0380.0468 .0224.0170 .0064.0110 .0028.0064 .0006.0016 Per.Ord. - Int.Per. .0600*.0000 .0872*.0004 Agu.0012.1078* .1542*.0028* .1958*.0056* .0062*.1706* .1322*.0018* .0978*.0006 .0784*.0000 .0540*.0000 1- 1 Per. - Ord. .0586* .0870* .1072* .1522* .1940* Aza, .1334* .0988* .0794* .0546* -.:,...... ,.4 -, -413 Per. - Per. .0006 .0040 .0076 .0180 .0386 .0396 .0180 .0062 .0032 .0008 Interval OrdinalSample A Percentile Descriptions of Samples Interval50.011 49.952OrdinalSample B Percentile 49.680 MeanMeansSD of of MeansSDs Means 49.990 3.1971.796 49.928 3.3161.786 24.71812.96849.476 4.3661.271 4.4611.249 30.5848.214 MeanSD of ofSDs Skews -0.432 1.658 -0.311 1.290 0.0066.900 4 0.0091.787 0.0051.321 0.0153.3530.423 SDMean of ofKurtosisSkews Kurtosis -0.924 0.5960.603 -0.962 0.6111.407 -1.121 0.5260.592 2.3001.2271.169 -0.115 0.8401.733 -1.249 0.426 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF TABLE A -_128 SIGNIFICANCE FOR A Scales B .0010 Negative Skewed .0050 .0100 (N = 5 ) and Leptokurtic .0250 Levels of Significance .0500 .0500 (N =15 ) .0250DISTRIBUTIONS .0100 .0050 .0010 Int.Int. - -Ord. Int. .0000 .0002 .0004.0004 .0014*.0020* .0062*0046* .0066*.0036* .0012*.0022 * .0010.0006 .0008.0004 .0002 Ord.Int. - Per.Int. .0000.0002 .0004 .0006.0008 .0014*.0026* 0054*.0076* .0038*.0064* .0014*.0020* .0008.0006 .0004 .0002 Ord.Ord. - -Ord. Per. .0002.0000 .0004 .0008.0004 me.0024* .0072*.0064* ..0062* .0064* .0020*.0024* .0008.0012 .0004.0008 .0002.0002 to 1 Per. - Int. .0066 .0156 .0256 lle Dale .0756* .0494* .0290 .0186 .0068 r~,, Per. - Ord. .0096 .0212 .0334* .0636* .0998* .0946* .0646* .0370* .0234 .0102 al Per. - Per. .0004 .0020 Sample A 0040 .0144, Descriptions of Samples .0356 .0346 .0152 Sample B .0068 .0034 .0008 SDMeans of Meansof Means Interval50.036 1.792 49.984Ordinal 1.765 Percentile 12.80949.896 Interval50.271 6.500 Ordinal50.094 4.681 Percentile50.228 8.833 MeanSD of ofSDs SkewsSDs -0.446 1.6723.203 -0.322 1.3023.309 -0.00624.819 6.943 22.180 0.0139.248 -0.00317.115 3.521 33.107 0.0033.670 MeanSD of KurtosisSkews -0.907 0.6020.601 -0.951 1.6140.605 -1.108 0.6000.532 2.3231.1071.212 -0.416 0.9990.632 -1.241 0.4140.403 TABLE OBTAINED PERCENTAGES OF t Negative Skewed (N =15 VALUES FOR GIVEN) and LEVELSLeptokurtic OF SIGNIFICANCE FOR R - 129 (N =5 ) DISTRIBUTIONS A Scales B .0350*.0010 .0658*.0050 .0922*.0100 .1384*.0250 Levels of Significance .1872*.0500 .1832*.0500 .0250 .0894*.0100 .0664*.0050 .0372*.0010 Int. - Ord.Int. .0396* .0666* .0896* .1270* .1662* .1820* .11118* um' .0952*.1090* .0890*.0730* .0420*.0602* Ord.Int. - -Int. Per. .0364*.0580* .0666*.0878* .0934*.1040* .1406*.1400* .1886*.1760* .1806*.188e _1307*Lae .0926*.0878* .0700*.0654* .0416*.0350* Ord. - Per.Ord. .0588*.0394* .0696*.0882* .1048*.0914* .1406*.1276* .1768*.1682* Aur .1876*,2346, .1486* .0042.1084* .0894* .0002.0594* 1 Per. - Ord.Int. .0000 .0006.0016 .0016.0046 .0088.0154 .0218*.0340 .0218*.0290* .Q076.0178 .0016 .0012 .0004 N Per. - Per. .0014 .0106 Sample A .0164 .0372 Descriptions of Samples .0686 .0684 .0392 Sample B .0190 Aug.0106 .0030 SDMeans of Meansof Means Interval50.007 1.055 49.945Ordinal 1.041 Percentile 49.612 7.487 Interval 11.22550.189 Ordinal49.823 8.049 Percentile49.80815.313 MeanSD of SDsSkews -0.981 1.1253.714 -0.614 0.7913.756 27.647 0.0143.487 -0.00312.16918.748 -0.01615.074 5.633 29.797 0.0057.786 'SD of KurtosisMeanSD of SkewsKurtosis 1.7310.5170.604 -0.397 0.4871.149 -1.073 0.3910.429 -0.922 0.6150.751 -1.048 0.5820.665 -1.148 0.5860.624 TABLE JEL,.....230 OBTAINED PERCENTAGES OF t VALUES FOR GIVENLeptokurtic LEVELS OF SIGNIFICANCE FOR (N = 5 ) and Lepoturtic (N =5 ) DISTRIBUTIONS Int. - Int. A Scales B .0012.0010 .0044.0050 .0072.0100 .0250 Levels of Significance .0442.0500 .0416.0500 .0186.0250 .0058.0100 .0026.0050 .0010 Int. - Per.Ord. .0012 .0250*.0060 .0126*.0104 Alaa.0478*.0224 .0698.0464 * .0695*.0452 .0476*.0224 0082.0304* .0234.0944 ma.0130.0008 Ord.Ord. - -Int. Ord. sub.0016 .0058.0052 .0102.0096, .0242.0270 .0496.0498 .0470.0438 .0230.0206 .0084.0092 .0046.0036 .0004.0006 w Per.Ord. - Int.Per. .0144 .0136.0014 .0248*0254* .0350*.0230* .0504*.0476* 0722*.0688 .0634.0700* .0422.0468* .0276.0300* .0200.0240 .0124.0100 L.)1-,o Per. - Ord. .0142 .0252* .0348* .0502* .0726* .0636 .0422 .0278.0104 .0060.0198 .0014.0096 Per. - Per. .0020 Interval Ailedi OrdinalSample A .0130 Percentile.0286 Descriptions of Samples .0532 .0502 Interval .0268 OrdinalSample B Percentile MeanMeansSD of of MeansSDs Means 50.014 2.2443.740 49.953 3.9532.202 27.67249.66014.199 50.016 2.2083.657 49.959 2.1903.912 14.33549.72727.599 MeanSD of ofSDs Skews 0.0012.504 -0.001 1.922 0.0077.042 0.0112.402 0.0051.895 0.6570.0147.027 MeanSDSD of Kurtosis of Skews -0.896 0.7680.638 -1.024 0.8350.679 -1.137 0.5790.647 -0.9050.7660.659 -1.039 0.6841.542 -1.132 0.592 TABLE B - 131 SIGNIFICANCE FOR OBTAINED PERCENTAGES OF t VALUESLeptokurtic FOR GIVEN LEVELS OF (N =5 ) and Leptokurtic of Sign1cicance (N =5 ) DISTRIBUTIONS A Scales B .0010 .0050 .0100 ...11322.0250 .0500.J10546 .0599.0500 ...031.4.0250 .0100 .0050.0134 .0010.0074 Int. - Ord.Int. .0100.0096.0076 .0190.0176.Q114 .0284.0234.0184 .0464*.0350 .0684.0590 .0604.0698* .0480*.0344 AM.0294*.0234 .0222.0178 .0124.0108 Ord.Int. - Int.Per. ,0066 .0128 .0178 .0328 .0552 .0522.0592 .0342.0310 .0178.0226 .0174.0130 .0066.0104 Ord. - Per.Ord. .0078,.0098 .0200.0178 .0282.0234 .0458*.0358 .0600.0684 .0698* .0466* .0300*.0142 .0214.0092 .0038.012(i Per. - Int.Ord. .0052.0060 .0136.0138 .0224.0194 .0366.0394 .0630.0602 .0584.0560 .0330.0318 .0158 .0076.0096 .0036.0024 Per. - Per. .0018 Interval .0074 OrdinalSample A .0134 Percentile.0262 Descriptions of Samples .0524 .0486 Interval .0254 OrdinalSample B .0120 Percentile MeansSD of of Means Means '2.23649.997 49.951 2.205 49.58527.44014.385 49.95618.63111.030 49.89215.051 7.985 29.82215.34449.722 MeanMeanSD of ofSDsSDs Skews 0.002'-2.3843.658 0.0111.8353.888 0.0217.238 11.999 0.013 0.0245.604 0.0247.719 MeanSDSD of of Skews Kurtosis -0.8870.7780.664 -1.036 0.6761.549 -1.143 0.5870.645 -0.917 0.6180.755 -1.042 0.5850.672 -0.953 9.5120.636 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR TABLE R - 132 A Scales B .0010 Leptokurtic .0050 .0100 (N = 15) and .0250 Levels of Significance .0500 .0500 (N =15) DISTRIBUTIONS .0250 .0100 .0050 .0010 Int. - Ord.Int. .0006.0002 .0030.0036 .0072.0070 .0216.0779 .0464.0496 .0500 0449 .0220.0202 .0080.0058 .0030.0038 .0004.0002 Ord.Int. - Per.Int. .0006.0026 .0046.0082 .0084.0134 .0250.0298 .0526.0486 .0416.0568 .0210.0338 0158.0064 .0022.0110 .0006.0044, Ord. - Per.Ord. .0026.0006 .0086.0046 .0138.0084 .0286.0248 .0510.0496 .0560.0436 .0338.0230 .0160.0082 .0106.0042 .0044.0008 =1- Per. - Ord.Int. .0030.0028 .0112.0116 .0160.0164 .0324.0338 .0556.0558 .0512.0502 .0244.0236 .0120.0118 .0066.0068 .0032.0030 ejt Per. - Per. .0010 .0058 Sample A .0112 .0256 Descriptions of Samples .0504_ .0474 .0226 Sample B .0098 .0060 .0010 SDMeans of Meansof Means Interval,50.003 1.280 49.947Ordinal 1.260 Percentile 49.647 8.227 Interval49.997 1.272 49.948Ordinal 1.258 Percentile 49.746 8.253 MeanSD of SDsSkewsSDs 0.0074.4021.889 0.0041.3984.501 30.645 0.0203.312 -0.026 1.8694.383 -0.016 1.3754.483 30.601 0.0093.352 MeanSD of SkewsKurtosis 2.3431.1371.223 -0.097 1.8030.861 -1.252 0.4190.423 2.3231.1331.212 -0.112 1.7920.847 -1.252 0.4280.420 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE TABLE B,_133 FOR Scales B .0010 Leptokurtic .0050 .0100 (N = 15) and Leotokurtic .0250 Levels of Significance .0500 .0500 (N .115) .0250DISTRIBUTIONS .0100 .0050 .0010 Int. - Ord.Int. A .0020.0014 .0058, .0120.0102 Qat.0276 .0514.0520 .0592.0470 .0330.0216 .0140.0082 20076_Drisa .0012.0010 Ord.Int. - -Iht. Per. .0016.0040 OSA.0058.0100 ,0164.0104 .0254.0310 .0530.0528 .0580.0458 .0210.0328 .0092.0170 .0042,.0104 .0008.0030, Ord.Ord. - -Ord. Per. .0040.0022 .0100.0080 Akat.0166 MK.0306 .0536.0526 .0570.0572 .0304.0336 .0172.0148, .0102.0072 .0026.0010 w 1 Per. - Int. .0012 .0064 .0104 .0258 .0550 .0488 .0252 .0120 .0068 .0018 L..)1- Per. - Ord. .0012 .0056 .0098 .0250 .0504 .0524 .0280 Alia .0088 .0018 Per. - Per. .0006 Interval .0042 OrdinalSample A .0098 Percentile.0240 Descriptions of Samples .0480 .0524 Interval .0284 OrdinalSample B ALla Percentile .0064 .0006 MeanSDMeans of ofMeansof SDs Means 50.030 4.4171.286 49.979 4.5011.259 30.66049.836 8.252 22.04549.998 6.402 49.85717.013 4.679 33.11249.754 8.934 MeanSD of ofSDs Skews 0.0161.9171.220 0.8470.0141.384 0.4260.0103.389 -0.003 1.1939.176 0.6310.0123.429 0.4070.0153.633 MeanSD of KurtosisSkews 2.3241.145 -0.111 1.762 -1.254 0.429 2.2771.053 -0.442 0.996 -1.236 0.420 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR TABLE _IL:7_134 A Scales B .0010 Leptokurtic .0050 .0100 = 5 ) and Leptokurtic .0250 Levels of Significance .0500 .0500 = 15) DISTRIBUTIONS .0250 .0100 .0050 .0010 Int. - Ord.Int. .0008.0010 .0Q32.0046 .0070.0088 .0230 1 .0444.0376 .0462 0494 .0214.0194 .Q082.0076 .0044.0030 10211.0002 Ord.Int. - -Int. Per. .0028.0006 .0090.0008 .0138.0010 Aga!'Alfa 0284 AWL!'.0550 ADM,.0504 .Q256.028* .0126.0010 .0002.0060 .0000.0016 Ord. - Ord. .0016.0006 .0096, .0024*.0240, .0070*.0438 .0086*.0466 .0028*.0238 .0010.0092 .0000.0062 .0000.0004 w Per.Ord. - Per.Int. .0590* Aga.0008.0800* .0960*.0010 .1340* .1732* .1694* .1308*.1288* .0958*.0976* .0786* .0514*.0508* .4: Per. - Per.Ord. .0590*.0014 .0058.0798* .0098.0954* .0258.1326* .0472.1724* .0494.1692" .0252 .0124 .0060 .0014 .~ Interval OrdinalSample A Percentile Descriptions of Samples Interval OrdinalSample B Percentile49.532 MeanSDMeans of ofMeansof SDsMeans 50.014 2.1863.726 49.956 2.1293.949 13.97149.79027.771 49.973 4.3931.291 49.926 4.4861.270 30.5748.265 MeanSD of SDsSkews -n,002 2.460 -0.006 1.902 0.0117.138 -0.001 1.875 0.0071.374 0.4220.0273.356 MeanSD of Kurtos1.3KurtosisSkews -0.905 0.7650.649 -1.024 0.6761.901 -1.148 0.5750.639 2.2821.1251.206 -0.118 0.8371.736 -1.249 0.431 TABLE R - 135 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LeptokurticLEVELS OF (N = 5 ) and Leptokurtic (N 1=15 ) SIGNIFICANCE FOR DISTRIBUTIONS Int. - Int. A Scales B .0000.0010 .0002.0050 .0100 .0018*.0250 Levels of Significance .0052*.0500 .0058*.0500 .0022*.0250 .0006,.0100 .0050.0002 Affla.0010 Int. - Per.Ord. :0000.0000 .0000.0002 .0000.0006.0008 .0022*.0026* .Q070*.0064* 0074*.0078* .0026*.0028* .0010.0008 .0002.0006 .0002.0000 Ord. - Int.Ord. .0000 .0004.00044 ' .0008.0908 .0028*.0022* .0066.*0086* .0084*.0054* .0032*.0022* .0008.0006 .0002.0004 .0000.0000 Per.Ord. - -Int. Per. .0000.0116 .0000.0242* .0350*.0006 .0614*.0026* .0910*.0062* .0076*.0878* .0030*.0572* .0316*.0010 .0212.0006 .0086.0000 m Per. - Ord.Per. .0160.0014 .0342*.0038 .0478*.0090 .0224.0726* .0454.1064* .1082*.0450 .0238.0712* .0426*.0090 .0296*.0046 .0006.0134 Interval OrdinalSample A Percentile Descriptions of Samples Interval OrdinalSample B Percentile 49.771 MeanMeansSD of of MeansSDs Means 50.029 3.7322.209 49.971 3.9512.183 27.67314.11549.800 49.87922.0356.360 49.83017.0514.695 33.082 8.988 MeanSD of ofSDs Skews -0.004 2.491 -0.007 1.927 0.0007.088 -0.028 9.261 -0.010 3.493 0.0220.4083.645 MeanSDSD of of Skews Kurtosis -0.899 0.6370.765 -1.028 0.6740.834 -1.141 0.6420.576 1.1782.2511.017 -0.432 0.6301.006 -1.233 0.425 OBTAINED PERCENTAGES OF t VALUES FOR GIVEN LEVELS OF SIGNIFICANCE TABLE .1._=_136 FOR Scales .0010 Leptokurtic .0050 .0100 (N 2. 15) and .0250 Levels of SignificanceLeptokurtic .0500 .0500 (N .. 5 ) DISTRIBUTIONS.0250 .0100 .0050 .0010 Int. - Ord.Int. A B .0378*.0336* _ns74*n617* .079* .1196* ..1210, .1684*.1722* .1292*.1274* .0916*.0858* .0702*.0628* .0346*.0400* Ord.Int. - -Int. Per. .0334*.0566* .0566*ope _me.0774*.0280, .1350*.1166*.1206* .1768*.167e.1706* .1720*.1848* .1256*.1504* .0826*.1108* .0600*.0910* .0318*.0642* Ord. - Per.Ord. .0568*.0376* .0802*.0604* .0998*.077Q* .1368*.1184* .1768*.1620* .1670*.1832* .1490*.1286* .1094*.0898* .0674*.0910* .0638*.0376* to t Per. - Int. .0008 .0014 .0024 .0096 .0246* .0216* .0098 .0038 .0018 .0002 a%t..11- Per. - Ord. .0002 .0012 .0022 .0068 .0154* .0154* .0048* .0022 .0014 .0012.0002 Per. - Per. .0018 Interval .0060 OrdinalSample A .0138 Percentile.0286 Descriptions of Samples .0540 .0566 Interval .0300, OrdinalSample B .0108 Percentile .0050 MeanMeansSD of of MeansSDs Means 49.976 4.3851.252 49.921 4.4821.234 49.50530.6298.098 18.68110.96750.012 49.79415.0978.025 29.83415.32549.611 MeanSD of SDsSkews -0.012 1.859 -0.006 1.381 0.0243.383 -0.00412.262 -0.016 5.664 0.6280.0007.766 MeanSD of KurtosisSkews 2.3071.1421.214 -0.123 1.7460.837 -1.257 0.4180.437 -0.924 0.6140.756 -1.046 0.5810.672 -1.148 0.567 APPENDIX C

TABLES OF SAMPLING DISTRIBUTIONS OF THE PRODUCT

MOMENT CORRELATION COEFFICIENT OBTAINED PERCENTAGES OF r VALUES FOR GIVEN LEVELS OF SIGNIFICANCE TABLE C - 1 FOR A Scales B .0010 .0050Normal .0100 (N =5 .0250 ) and Levels of Significance Normal .0500 .0500 (N = 5 ) DISTRIBUTIONS.0250 .0100 .0050 .0010 Int.Int. - Int.- Ord. A008 _nn42.0048 -alo. -azuArsn .0450 .0462.0440 AZIC.0224 A076.0076 .0036.0034 4201 Ord.Int. - -Int. Per. .0004_nniR u .nn42_rm. SKIMADA&_nan _022k 0276 JAIL.0470.0436 .0454.0460 ,02l0.0222 ,0212..007_4 ,gall.0034 Awl_00p4 Ord.Ord. - -Ord. Per. .0012.0008 .0047.0046 .0080.0076 Aza,0222. .0454.0424 .0456.0454 .0218.0198 .0080.0068 .0034 Apia.0004 I-,o I Per. - Int.Ord. .0010L0001 A011.0040 .0086.0092 jig/.0248 .0456.0454 .0434.0418 .0212 aimm.0076 .0036.0022 .0010.0006 Per. - Per. .0010 .0046 Sample AAfail .0236 Descriptions of Samples .0462 .0434 ,0201 Sample B .0068 .0028 .n010 SDMeans of Meansof Means Interval50.003 1.807 Ordinal49.941 1.804 Percentile 12.99049.564 Interval49.997 1.798 Ordinal49.924 1.791 Percentile 12.87049.452 MeanMeanSD of ofSDs Skews -0.011 1.1993.360 -0.009 0.9873.428 -0.00524.721 6.907 -0.001 1.2073.401 -0.003 0.9793.457 24.907 0.0066.852 SDMean of ofKurtosisSkews Kurtosis -0.998 0.6140.507 -1.075 0.5940.615 -1.106 0.5200.594 -0.993 0.6090.494 -1.062 1.1640.593 -1.109 0.5150.588 TABLE C - 2 OBTAINED PERCENTAGES OF r VALUES Normal 01 = 5 ) and FOR GIVEN Normal LEVELS OF SIGNIFICANCE (N =5 ) DISTRIBUTIONS FOR Int. - Int. A Scales B .0010 .0050 .0100 .0250 Levels of Significance .0538.0500 .0544.0500 .0250 .0100 .0050 .0010 Int. - Ord. .0004.0010 A046.0056 .0104 xer...... 0254^07n .0520 .0554 .0262,0261 lQa.0102 .0049.0048 .0006 Ord.Int. - -Int. Per. A001,.0010 .0042.0052 .0092.0116 A25/.0254 .0532.0524 .0562.0566 .0268.0240 .0092.0090 Alui.0044 Agia.0010.0004 Ord. - Per.Ord. .0004.0006 .0054.0044 .0100.0094 .0268.0256 .0522.0516 m66.0558 .0272.0266 .0100.0086 ,0051.0050 .0008.0004 P3o 1 Per. - Int.Ord. .0006 .0040 ,008Q.0092 .0256.0262 .0498.0530 A0558.0538 .0272.0270 ,0100.0106 .0048.0050 Am&.0008 Per. - Per. ,0007,020L .0054 Sample A.0108 .0256 Descriptions of Samples ,0578 .0552 .0262 Sample B ,0106 .0054 .am& SDMeans of Meansof Means Interval 50.007 1.822 Ordinal49.940 1.809 Percentile 49.57212.994 Interval50.056 7.321 49.772Ordinal7.160 Percentile 49.63912.782 MeanSD of ofSDs SDsSkews 0.0031.231.3.386 0.0050.9903.440 24.773 0.0076.918 -0.00113.900 5.123 13.517 0.0025.130 -0.00024.936 7.011 SDMean of ofKurtosisSkews Kurtosis -0.994 0.5130.615 -1.079 0.5490.595 -1.101 0.5260.599 -1.002 0.5010.617 -0.988 0.5110.630 -1.117 0.5200.592 OBTAINED PERCENTAGES OF r VALUES TABLE FOR GIVEN C - 3 LEVELS OF SIGNIFICANCE FOR A Scales B .0010 .0050.Normal .0100 (N =15 ) and .0250 Levels of SignificanceNormal .0500 .0500 (N ) DISTRIBUTIONS.0250 .0100 .0050 .0010 Int. - Ord.Int. .0010 .0032.0042 .0064 .019012171 Ank.0390 .05820578 .0296.0294 .0130 ..2022..0080 .0014.0008 Int. - Per. A012.0006 .0030.0026 Mb .0200 .0370.0374 .0582 ,0294 A1122..1013.Ala AM...0022 .2012. Ord. - Int. MaAl151 -...,_ ,0294 -QUI Ord. - Per.Ord. AMC.0004 .0026.0024 ,000Aakk Auk.0176.0180 .0362.0372 Aga160Mak .nu.0304 AukAla .0068-0670 .0016-0020 4,,0 1 Per. - Ord.Int. ,QQQL.0004 .0026,.0032 .0050.0062 , .0184.0162 .0374.0358 .0580,.0572 .0298.0310 ,10125..0138 .0072.0072 0011 Per. - Per. .0008 .0028 Sample A .0058 .0188 Descriptions .0364 of Samples .0608 .0306 Sample B .0136. .0068 U&.0016 SDMeans of Meansof Means Interval50.002 1.027 49.937Ordinal1.024 Percentile 49.534 7.374 Interval50.008 1.031 49.947Ordinal1.028 Percentile 49.614 7.402 MeanSD of ofSDs SDsSkews -0.002 0.7103.803 -0.001 0.5143.830 27.579 0.0073.514 -0.009 0.7163.798 -0.006 0.5163.826 -0.00027.533 3.518 SDMean of ofKurtosisSkews Kurtosis -0.383 0.7850.526 -0.969 0.4800.373 -1.047 0.4320.384 -0.375 0.7820.521 -0.965 0.4780.371 -1.043 0.4290.382 OBTAINED PERCENTAGES OF r VALUES FOR GIVEN TABLE C - 4 LEVELS OF SIGNIFICANCE FOR A Scales B .0010 .0050 Normal .0100 - (N .=15 ) and .0250 Levels of SignificanceNormal .0500 .0500 (N =15 ) DISTRIBUTIONS .0250 .0100 Int.Int. - -Ord. Int. _mon.0008 .0014.nnu .0060.0072 .0214.0222 .04R9 _0560 ,0288 .0128 .0068.0050 .0010 Ord.Int. - Int.- Per .0008.0006 .0040J1040 -.0064 .0202 .0456.a466 .0576A564 Jima.0104 .0130 MEI.0070 Alla.0012 Ord. - Per.Ord. .0006.0008 .0040.0034 ACM.0084.0072 .0210.0222 .0456.0500 .0546.0560 .0296.0278' Ala .0060.0060 .0010.aam Per.Per - Ord. - Int. '-'411116- .0034.0044 ,fflia.0074 .0232.0222 ,042z.0488 .0546.0552 .0278Mall Ana.0114.0128 .0066.0070 AO&.0010 Per. - Per. 4 Q11,.0006 .0042 Am. _022.4..0226 Descriptions of Samples .0462.0474 .0546.0564 .0294 .0128.0124 .0066.0064 .0008.0010 SDMears of Meansof Means Interval49.989 49.921OrdinalSample A Percentile 49.440 Interval49.990 .Sample49.719Ordinal B Percentile 49.556 MeanSD of SDs 0.7253.8171.023 0.5203.8351.025 27.605 3.5327.377 15.514 3.0294.269 15.163 3.0574.182 27.565 3.6597.538 SDMean of ofSkews Skews 0.005 12...3750.002 0.013 -0.010 -0.010 0.005 MeanSD of Kurtosis -0.363 0,7780.526 -0.961 0.475 -1.041 Q.4210.384 -0.368 0.7700.517 -0.266 0.8240.554 -1.038 0.4470.385 ...... , OBTAINED PERCENTAGES OF r VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR TABLE C - 5 A Scales B .0010 .0050Normal .0100 (N = .0250 andPositive Skewed(N = 5 ) Levels of Significance .0500 .0500 .0250 DISTRIBUTIONS .0100 .0050 -.0010 Int. - Ord.Int. JSQL .0046 ,01126..0106 .0244.0240 .0520.0546 ,alla O lO .1216..0246 .30210..0090 .0046.0042 -ODE 0004 Ord.Int. - Per.Int. Ma.0014.0004 ,0046.0048 .009& .0248.0244 .0S14.0560 Alm..0530 .0256.0248 ni.0084 A20.0040 .0010.0010, Ord.Ord. - -Ord. Per Aink.0006 .0042 A111ADA.0096, ,0260.0270 _mu.0524 .0528.0526 .0236.0252 .0104- Alla.0042 Ami.0000 Per. - Ord.Int. .0012.0010 Ma.0040.0946 .0110.0106 .0260.0228 2522.0544 .0528 .0250.0244 .0098.0086, ,0044.0040 .0008,.0006, Per. - Per. .0006 .0052 Sample A4104, .0258 Descriptions of. Samples .0530 Alm.0522 .0256 Sample B .0104 4048, .0006 SDMeans of Meansof Means Interval50.013 1.795 49.944Ordinal 1.792 Percentile 12.89649.585 Interval49.959 2.590 `Ordinal49.996 2.185 Percentile 49.968 4.861 MeanMeanSD of ofSDs Skews 0.0121.2163.343 0.0130.9983.418 24.641 0.0156.979 0,4221.6293.167 0.3071.2833.328 24.883 0.0076.806 MeanSD of KurtosisSkews -0.996 0.5060.617 -1.071 0.5730.602 -1.102 0.5250.597 -0.938 0.594n.597 -1.018 0.6510.605 -1.126 0.5260.594 OBTAINED PERCENTAGES Normal (N = 5OF ) randPositive VALUS FOR Skewed(NGIVEN LEVELS = 5 )OF DISTRIBUTIONS SIGNIFICANCE FOR TABLE C - 6 A Scales B .0010 .0050 ' .0100 .0250 Levels of Significance .0500 .0500 .0250 .0100 .0050 .0010 Int.Int. - Ord.- Int. .0008,AR04 .n052.0044 Ma Auz .0266 .0496.0494 '.0520.0498 .0282.0272 .0100.0094 .0042 nno Am_.0010 Ord.Int. - -Int. Per. .0004.0006 .0046.0056 Alm.0098.0122 .0254 .0508.0506 ILL .0250 Agla .0048.0050 ..ma .0004 Ord. - Per.Ord. .0006.0006 A072.0048 .0118.0112 Aga-.0250 Ala .0502, ,gaik.0496.0506 .0266.0264 .0108.0100 Jima.0050 .0016.0004 cr.C3 Per.Per. - -Ord. Int. .0008.0006 .0054.0044 Apin.0114 .0246.0238 .0502.0514 .0522..0496 .0274.0258 .0088.0104 .0042 .0004 Per. - Per. ,Qua Sample A .0120 .0250 Descriptions of Samples .0512 .0506 .0254 Sample B .0112 gg.0046 .0008 SDMeans of Meansof Means Interval50.040 1.811 Ordinal49.972 1.796 Percentile 49.78512.898 Interval49.934 8.884 Ordinal49.326 7.295 Percentile 13.51149.294 MeanMeanSD of ofSDs Skews 0.0021.2293.379 -0.000 0.9983.437 24.745 0.0026.951 15.8000.4288.115 13.476 0.3695.688 26.256 0.0437.216 MeanSD of KurtosisSkews -0.996 0.5100.615 -1.068 0.6550.597 0.519-1.1070.592 0.576-0.9360.592 -0.964 0.5620.593 -1.132 0.5260.588 OBTAINED PERCENTAGES OF r VALUES FOR GIVEN LEVELS or SIGNIFICANCE FOR Normal (N = 15) andPositive Skewed(N =15 ) DISTRIBUTIONS TABLE C - 7 Int. - Int. A Scales B .00100006 .0040.0050 .0100.0100 .0276.0250 Levels of Significance .0510.0500 .0440.0500 .0190.0250 .0092.0100 .0056.0050 .0008.0010 Int. - Ord.Per .0014.0006 .0060.0050 .0104.0112 .0278.0264 .0492.0494 .0458.0434 .0218.0190 .0090.0092 .0046.0052 .0010 Ord. -tOrd.- Int. .0012..0008 .0052.0044 .0102 .0278.0266 .0502.0492 .044Q.0426 .0202.0212 .0098.0074 .0042.0034 .0010 Per.Ord. - Int.Per. JNINLAMU& .0051.0048 Ala.0104 ...0214.0260 .0494.0516 .0432.0472 .0200.0212 ,0016.0078 Auk.0042 .0010.0016 J Per. - Per.Ord. ,0016 .0.01515..0054 .0122 .0296.0276 .0522.0506 y§.2.0446 .0214.0206 4291.0094 .0038.0040 .0014.0010 .." AWL Sample A Descriptions of Samples Sample B ..,..i MeansSD of of Means Means Interval49.988 1.029 49.917Ordinal 1.026 Percentile 49.408 7.379 Interval49.997 1.027 50.033Ordinal 1.027 Percentile50.226 7.461 MeanSD of SDsSkews 0.0200.7203.806 0.0140.5153.830 25.574 0.0213.523 0.9781.1023.709 0.6110.7943.780 27.675 0.0043.447 SDMean of ofKurtosisSkews Kurtosis -0.375 0.7810.520 -0.971 0.3670.464 -1.045 0.3810.425 1.6790.4950.593 -0.409 0.4841.131 -1.060 6.020.389 OBTAINED PERCENTAGES OF r VALUES FOR GIVEN Normal (N =15 ) andPositive Skewed(N =15 ) DISTRIBUTIONS TABLE c - LEVELS OF SIGNIFICANCE FOR Int. - Int. A Scales B .0014.0010 .0066.0050 .0120.0100 .0304.0250 Levels of Significance .0534.0500 .0462.0500 .0252.0250 .0100.0098 .0046.0050 '.0006.0010 Int.Int. - Per.- Ord. .0014.0012 .0062.0058 .0112.0116 .0282.0288 .0554.0558 .0476.0480 .0218.0240 .0094.0110 .0042.0052 .0008 Ord. - Ord.Int. .0010 .0056.0052 .0112.0106 .0288.0286 .0538.0524 .0464.0464 .0262.0238 .0108.0098 .0052.0050 .0010.0006.0010 Per.Ord. - -Int. Per. .0012.0014 .0054.0072 .0106.0124 .0276.0272 .0334.0536 .0474.0478 .0252.0234 .0092.0106 .0054 .0020 ce Per.Per. - -Per. Ord. .0012.0012 .0072.0054 .0116.0112 .0288.0286 .0546.0540 .0492.0470 .0262 .0102 .0050 .0008.0004 Interval OrdinalSample A Percentile Descriptions of Samples Interval .0238 OrdinalSample 3 .0100 Percentile .0054 .0024 MeanSDMeans of MeansSDsof Means 50.002 3.7861.016 49.940 1.0163.819 27.48549.542 7.303 18.55350.043 5.134 15.51148.404 4.223 29.20346.383 7.824 MeanSD of SkewsSDs -0.004 0.725 -0.002 0.521 0.0063.556 0.9995.574 0.8023.457 0.0723.616 SDMean of ofKurtosis Kurtosis -0.372 0.7780.523 -0.959 0.4840.372 -1.0400.4380.383 1.7690.5430.610 1.2180.0200.494 -1.085 0.4390.389 OBTAINED PERCENTAGES or r VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR TABLE C - 9 Scales B .0010 Positive Skewed (N = 5 .0050. .0100 .0250 ) and Negative SkewedN Levels of Significance .0500 .0500 5 ) DISTRIBUTIONS .0250 .0100 .0050 .0010 Int.Int. - -Int. Ord. A .0012.0016 .0052.0074 .0116.0124 .0298.0312 .0556.0600 .0410..0464 .,9116 .0216 .0056.0070 .00402222 .0304.0004 Ord.Int. - -Int. Per. .0014.0004 .0070.0042 .0124.0088 .0290.0212 .0560.0444 .0460.0570 .0216.0264 ,0222 .0072 ,D2144 .0032 .0008.0004 Ord.Ord. - -Ord. Per .0006,.0012 .0056 .0074.0108 .0224.0264 .0448.0530 .0554.0472 .0284.0250 .0088 .0054.0034 ,201.6 .0006 Per.Per - Ord. - Int. .0012..0014 .0058IX.0052 .0098.0104 .0242.0232 .0484.0470 .0550.0550 .0294.0264 _nun .0116.0092' .0056.0032 .0008 Per. - Per. .0010 .0044 Sample A .0102 ' .0230 Descriptions of Samples .0456 .0558 .0304 Sample B .0122 .0054 .0012 ti Interval Ordinal Percentile Interval Ordinal Percentile49.622 MeansSD of of Means Means 49.954 1.797 ' 49.993 1.792 12.91149.966 50.013 1.777 49.951 1.762 12.811 MeanSD of ofSDs SkewsSDs 0.4361.6283.171 0.3171.2783.319 24.801 0.0136.953 -0.429 3.1911.628 -0.308 1.2703.317 24.845 0.0066.888 MeanSD of KurtosisSkewsKurtosis -0.913 0.6010.600 -1.016 0.8900.604 -1.107 0.5280.598 -0.932 0.6010.593 -0.967 1.4640.604 -1.126 0.5250.588 OBTAINED PERCENTAGES OF r VALUES TABLE FOR GIVEN C - 10 LEVELS OF SIGNIFICANCE FOR A Scales B .0010 Positive Skewed (N = 5 ) and .0050 .0100 .0250 Levels of NegativeSignificance Skewe(N .0500 .0500 = 5 ) .0250 DISTRIBUTIONS .0100 .0050 .0010 Int. - Ord.Int. .0016.0018 .0064.0066 .0130.0134 .0338.0348 .0622.0626 .0380.0378 .0166.0144 ,0060.0074 .0040.0038 .0008.0004 Ord.Int. - Per.Int. .0016.0010 .0068.0044 .0128.0096 .0304.0260 .0612.0508 .0404.0434 .0218 .0070.0104 .0044 .0006.0010 Ord.Ord. - -Ord. Per. .0016.0010 .0042.0062 .0110.0122 .0280.0298 .0502.0620 .0444.0408 M76.0226.0184 .0096.0080 .0048.00380011 .0008 1-+ Per.Per - Ord. - Int. .0006 .0048 .0126 .0270.G450 .0480.0474 .0500.0488 .0258.0238 .0108.0082 .0046.0042 .0014.0010 0 Per. - Per. .0012 .0042 Sample A.0110 .0252 Descriptions of Samples .0486 .0492 .0236 Sample B .0086 .102 .0010 MeansSD of of Means Means Interval49.984 1.782 50.017Ordinal 1.781 Percentile 12.81950.108 Interval50.030 9.074 51.192Ordinal 7.350 Percentile 13.75952.623 MeanSD of SDsSkewsSDs 0.4341.6243.191 0.3081.2793.339 -0.00024:933 6.995 -0.42815.699 8.152 -0.37613.297 5.674 -0.02825.883 7.195 SDMean of ofKurtosisSkews Kurtosis -0.897 0.6160.603 -0.986 1.2860.606 -1.105 0.5290.602 -0.933 0.5770.596 -0.963 0.6510.596 -1.118 0.5300.600 OBTAINED PERCENTAGES OF r VALUES FOR GIVEN LEVELS OF SIGNIFICANCE FOR TABLE C - 11 A Scales B .0010 Positive Skewed .0050 .0100 (N =15 ) andNegative Skewed(N =15 ) DISTRIBUTIONS .0250 Levels of Significance .0500 .0500 .0250 .0100 .0050 .0010 Int. - Ord.Int. .0018.nn,, .0066.0078 ,0122.0110 .0264,.0310 .0518.0556 .0358.0298* .0108.0122 .0030.0022 .0016.0014 .0008.0002 Ord.Int. - Int.Per. ,0012.0018 .0054.0042 .0104.0092 .0252.0200 .0508.0444 .0348.0454 .0134.0194 .0024.0058 .0016.0022 .0006.0018 Ord.Ord. - -Ord. Per. .0016.0018 .0056 .0100.0102 .0212.0254 .0448.0488 .0440.0378 .0104.0158 .0062.0032 .0026.0018 .0016.0008 Per. - Ord.Int. .0008-.0012 .0050.0034 .0092.0076 .0202.0196 .0430.0436 .0438.0442 .0198.0194 .0060.0072 .0030.0028 .0006.0008 Per. - Per. .0022 .0056 Sample A .0110 .0230 Descriptions of Samples .0460 .0466 .0200 Sample B .0070 .0032 .0010 SDMeans of Meansof Means Interval 50.312 1.036 50.044Ordinal 1.033 Percentile 50.301 7.464 Interval49.992 1.023 Ordinal49.926 1.010 Percentile49.434 7.300 MeanSD of.of SkewsSDs 0.9861.1183.725 0.6150.8053.789 27.654 0.0013.533 -0.969 1.1313.716 -0.611 0.8083.763 27.600 0.0173.497 MeanSD of KurtosisSkews 1.7570.5350.610 -0.383 1.2090.498 -1.062 0.4380.386 0.4791.7290.607 -0.406 0.4881.167 -1.078 0.4270.380 TABLE C - 12 OBTAINED PERCENTAGES OF r VALUES Positive Skewed (N = 15) anctlesative FOR GIVEN LEVEL:3')F SIGNIFICANCE Skewed (N =15 ) DISTRIBUTIONS FOR A Scales B .0010 .0050 .0100 .0250 Levels of Significance .0500 1.- .0500 .0250 .0100 .0050 .0010 Int.Int. - -Ord. Int. .0024.0024 ADA.0094 -au&.0172 -.113Z6..0380 .0646 B612 .0399-0164 4-.0 .01.0150 40 .0046 .0024 .0004 Ord.Int. - -Int. Per .0016.0002 .0092.0046 .0148.0094 .0326.0240 .0580.0510 Aus.0412 .0192Imo .0058-0074mai _Duo-.01330.0028 -000A_wail.0006 Ord.Ord. - -Per. Ord. .0004.0018 .0052.0068 .0106.0130 .0236.0314 .0490.0604 .0494.0434 .0256.0176 .0084.0052 .0040.0018 .0004 01 Per. - Int. .0004 .0042 .0106 .0244 .0478 .0496 .0246 .C,116 .0050 .0018.0006 I.,1-. Per.Per. - -Per. Ord. .0004.0006 _004.0048 6 .0096.0088 .0258.0234 .0470.0498 .0524.0522 .0278.0248 .0106.0104 .0044.0050 .0012.0012 Means of Means Interval49.982 OrdinalSample A Percentile Descriptions of Samples Interval OrdinalSample B Percentile MeanSD of MeansSDs 3.6961.041 50.017 3.7751.039 27.67650.110 7.535 18.46750.062 5.177 '5.29551.276 4.174 28.96852.8087.699 SDMeanSD of of Skews ofSDs Skews 0.5940.9811.082 0.6140.772 0.0133.427 -0.990 5.687 -0.809 3.523 -0.046 3.640 SDMoan of Kurtosisof Kurtosis 1.7120.490 -0.417 1.1450.481 -1.065 0.4280.390 1.6960.4980.592 1.2270.0400.495 -1.0920.4240.385