Nonparametric Test Procedures 1 Introduction to Nonparametrics
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Binomials, Contingency Tables, Chi-Square Tests
Binomials, contingency tables, chi-square tests Joe Felsenstein Department of Genome Sciences and Department of Biology Binomials, contingency tables, chi-square tests – p.1/16 Confidence limits on a proportion To work out a confidence interval on binomial proportions, use binom.test. If we want to see whether 0.20 is too high a probability of Heads when we observe 5 Heads out of 50 tosses, we use binom.test(5, 50, 0.2) which gives probability of 5 or fewer Heads as 0.09667, so a test does not exclude 0.20 as the Heads probability. > binom.test(5,50,0.2) Exact binomial test data: 5 and 50 number of successes = 5, number of trials = 50, p-value = 0.07883 alternative hypothesis: true probability of success is not equal to 0.2 95 percent confidence interval: 0.03327509 0.21813537 sample estimates: probability of success 0.1 Binomials, contingency tables, chi-square tests – p.2/16 Confidence intervals and tails of binomials Confidence limits for p if there are 5 Heads out of 50 tosses p = 0.0332750 is 0.025 p = 0.21813537 is 0.025 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Binomials, contingency tables, chi-square tests – p.3/16 Testing equality of binomial proportions How do we test whether two coins have the same Heads probability? This is hard, but there is a good approximation, the chi-square test. You set up a 2 × 2 table of numbers of outcomes: Heads Tails Coin #1 15 25 Coin #2 9 31 In fact the chi-square test can test bigger tables: R rows by C columns. -
12.6 Sign Test (Web)
12.4 Sign test (Web) Click on 'Bookmarks' in the Left-Hand menu and then click on the required section. 12.6 Sign test (Web) 12.6.1 Introduction The Sign Test is a one sample test that compares the median of a data set with a specific target value. The Sign Test performs the same function as the One Sample Wilcoxon Test, but it does not rank data values. Without the information provided by ranking, the Sign Test is less powerful (9.4.5) than the Wilcoxon Test. However, the Sign Test is useful for problems involving 'binomial' data, where observed data values are either above or below a target value. 12.6.2 Sign Test The Sign Test aims to test whether the observed data sample has been drawn from a population that has a median value, m, that is significantly different from (or greater/less than) a specific value, mO. The hypotheses are the same as in 12.1.2. We will illustrate the use of the Sign Test in Example 12.14 by using the same data as in Example 12.2. Example 12.14 The generation times, t, (5.2.4) of ten cultures of the same micro-organisms were recorded. Time, t (hr) 6.3 4.8 7.2 5.0 6.3 4.2 8.9 4.4 5.6 9.3 The microbiologist wishes to test whether the generation time for this micro- organism is significantly greater than a specific value of 5.0 hours. See following text for calculations: In performing the Sign Test, each data value, ti, is compared with the target value, mO, using the following conditions: ti < mO replace the data value with '-' ti = mO exclude the data value ti > mO replace the data value with '+' giving the results in Table 12.14 Difference + - + ----- + - + - + + Table 12.14 Signs of Differences in Example 12.14 12.4.p1 12.4 Sign test (Web) We now calculate the values of r + = number of '+' values: r + = 6 in Example 12.14 n = total number of data values not excluded: n = 9 in Example 12.14 Decision making in this test is based on the probability of observing particular values of r + for a given value of n. -
Binomial Test Models and Item Difficulty
Binomial Test Models and Item Difficulty Wim J. van der Linden Twente University of Technology In choosing a binomial test model, it is impor- have characteristic functions of the Guttman type. tant to know exactly what conditions are imposed In contrast, the stochastic conception allows non- on item difficulty. In this paper these conditions Guttman items but requires that all characteristic are examined for both a deterministic and a sto- functions must intersect at the same point, which chastic conception of item responses. It appears implies equal classically defined difficulty. The that they are more restrictive than is generally beta-binomial model assumes identical char- understood and differ for both conceptions. When acteristic functions for both conceptions, and this the binomial model is applied to a fixed examinee, also implies equal difficulty. Finally, the compound the deterministic conception imposes no conditions binomial model entails no restrictions on item diffi- on item difficulty but requires instead that all items culty. In educational and psychological testing, binomial models are a class of models increasingly being applied. For example, in the area of criterion-referenced measurement or mastery testing, where tests are usually conceptualized as samples of items randomly drawn from a large pool or do- main, binomial models are frequently used for estimating examinees’ mastery of a domain and for de- termining sample size. Despite the agreement among several writers on the usefulness of binomial models, opinions seem to differ on the restrictions on item difficulties implied by the models. Mill- man (1973, 1974) noted that in applying the binomial models, items may be relatively heterogeneous in difficulty. -
Bitest — Binomial Probability Test
Title stata.com bitest — Binomial probability test Description Quick start Menu Syntax Option Remarks and examples Stored results Methods and formulas Reference Also see Description bitest performs exact hypothesis tests for binomial random variables. The null hypothesis is that the probability of a success on a trial is #p. The total number of trials is the number of nonmissing values of varname (in bitest) or #N (in bitesti). The number of observed successes is the number of 1s in varname (in bitest) or #succ (in bitesti). varname must contain only 0s, 1s, and missing. bitesti is the immediate form of bitest; see [U] 19 Immediate commands for a general introduction to immediate commands. Quick start Exact test for probability of success (a = 1) is 0.4 bitest a = .4 With additional exact probabilities bitest a = .4, detail Exact test that the probability of success is 0.46, given 22 successes in 74 trials bitesti 74 22 .46 Menu bitest Statistics > Summaries, tables, and tests > Classical tests of hypotheses > Binomial probability test bitesti Statistics > Summaries, tables, and tests > Classical tests of hypotheses > Binomial probability test calculator 1 2 bitest — Binomial probability test Syntax Binomial probability test bitest varname== #p if in weight , detail Immediate form of binomial probability test bitesti #N #succ #p , detail by is allowed with bitest; see [D] by. fweights are allowed with bitest; see [U] 11.1.6 weight. Option Advanced £ £detail shows the probability of the observed number of successes, kobs; the probability of the number of successes on the opposite tail of the distribution that is used to compute the two-sided p-value, kopp; and the probability of the point next to kopp. -
Jise.Org/Volume31/N1/Jisev31n1p72.Html
Journal of Information Volume 31 Systems Issue 1 Education Winter 2020 Experiences in Using a Multiparadigm and Multiprogramming Approach to Teach an Information Systems Course on Introduction to Programming Juan Gutiérrez-Cárdenas Recommended Citation: Gutiérrez-Cárdenas, J. (2020). Experiences in Using a Multiparadigm and Multiprogramming Approach to Teach an Information Systems Course on Introduction to Programming. Journal of Information Systems Education, 31(1), 72-82. Article Link: http://jise.org/Volume31/n1/JISEv31n1p72.html Initial Submission: 23 December 2018 Accepted: 24 May 2019 Abstract Posted Online: 12 September 2019 Published: 3 March 2020 Full terms and conditions of access and use, archived papers, submission instructions, a search tool, and much more can be found on the JISE website: http://jise.org ISSN: 2574-3872 (Online) 1055-3096 (Print) Journal of Information Systems Education, Vol. 31(1) Winter 2020 Experiences in Using a Multiparadigm and Multiprogramming Approach to Teach an Information Systems Course on Introduction to Programming Juan Gutiérrez-Cárdenas Faculty of Engineering and Architecture Universidad de Lima Lima, 15023, Perú [email protected] ABSTRACT In the current literature, there is limited evidence of the effects of teaching programming languages using two different paradigms concurrently. In this paper, we present our experience in using a multiparadigm and multiprogramming approach for an Introduction to Programming course. The multiparadigm element consisted of teaching the imperative and functional paradigms, while the multiprogramming element involved the Scheme and Python programming languages. For the multiparadigm part, the lectures were oriented to compare the similarities and differences between the functional and imperative approaches. For the multiprogramming part, we chose syntactically simple software tools that have a robust set of prebuilt functions and available libraries. -
1 Sample Sign Test 1
Non-Parametric Univariate Tests: 1 Sample Sign Test 1 1 SAMPLE SIGN TEST A non-parametric equivalent of the 1 SAMPLE T-TEST. ASSUMPTIONS: Data is non-normally distributed, even after log transforming. This test makes no assumption about the shape of the population distribution, therefore this test can handle a data set that is non-symmetric, that is skewed either to the left or the right. THE POINT: The SIGN TEST simply computes a significance test of a hypothesized median value for a single data set. Like the 1 SAMPLE T-TEST you can choose whether you want to use a one-tailed or two-tailed distribution based on your hypothesis; basically, do you want to test whether the median value of the data set is equal to some hypothesized value (H0: η = ηo), or do you want to test whether it is greater (or lesser) than that value (H0: η > or < ηo). Likewise, you can choose to set confidence intervals around η at some α level and see whether ηo falls within the range. This is equivalent to the significance test, just as in any T-TEST. In English, the kind of question you would be interested in asking is whether some observation is likely to belong to some data set you already have defined. That is to say, whether the observation of interest is a typical value of that data set. Formally, you are either testing to see whether the observation is a good estimate of the median, or whether it falls within confidence levels set around that median. -
Signed-Rank Tests for ARMA Models
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector JOURNAL OF MULTIVARIATE ANALYSIS 39, l-29 ( 1991) Time Series Analysis via Rank Order Theory: Signed-Rank Tests for ARMA Models MARC HALLIN* Universith Libre de Bruxelles, Brussels, Belgium AND MADAN L. PURI+ Indiana University Communicated by C. R. Rao An asymptotic distribution theory is developed for a general class of signed-rank serial statistics, and is then used to derive asymptotically locally optimal tests (in the maximin sense) for testing an ARMA model against other ARMA models. Special cases yield Fisher-Yates, van der Waerden, and Wilcoxon type tests. The asymptotic relative efficiencies of the proposed procedures with respect to each other, and with respect to their normal theory counterparts, are provided. Cl 1991 Academic Press. Inc. 1. INTRODUCTION 1 .l. Invariance, Ranks and Signed-Ranks Invariance arguments constitute the theoretical cornerstone of rank- based methods: whenever weaker unbiasedness or similarity properties can be considered satisfying or adequate, permutation tests, which generally follow from the usual Neyman structure arguments, are theoretically preferable to rank tests, since they are less restrictive and thus allow for more powerful results (though, of course, their practical implementation may be more problematic). Which type of ranks (signed or unsigned) should be adopted-if Received May 3, 1989; revised October 23, 1990. AMS 1980 subject cIassifications: 62Gl0, 62MlO. Key words and phrases: signed ranks, serial rank statistics, ARMA models, asymptotic relative effhziency, locally asymptotically optimal tests. *Research supported by the the Fonds National de la Recherche Scientifique and the Minist&e de la Communaute Franpaise de Belgique. -
The Exact Binomial Test Between Two Independent Proportions: a Companion
¦ 2021 Vol. 17 no. 2 The EXACT BINOMIAL TEST BETWEEN TWO INDEPENDENT proportions: A COMPANION Louis Laurencelle A B A Universit´ED’Ottawa AbstrACT ACTING Editor This note, A SUMMARY IN English OF A FORMER ARTICLE IN French (Laurencelle, 2017), De- PRESENTS AN OUTLINE OF THE THEORY AND IMPLEMENTATION OF AN EXACT TEST OF THE DIFFERENCE BETWEEN NIS Cousineau (Uni- VERSIT´ED’Ottawa) TWO BINOMIAL variables. Essential FORMULAS ARE provided, AS WELL AS TWO EXECUTABLE COMPUTER pro- Reviewers GRams, ONE IN Delphi, THE OTHER IN R. KEYWORDS TOOLS No REVIEWER EXACT TEST OF TWO proportions. Delphi, R. B [email protected] 10.20982/tqmp.17.2.p076 Introduction SERVED DIFFERENCE AND THEN ACCUMULATING THE PROBABILITIES OF EQUAL OR MORE EXTREME differences. Let THERE BE TWO SAMPLES OF GIVEN SIZES n1 AND n2, AND Our PROPOSED test, SIMILAR TO THAT OF Liddell (1978), USES AND NUMBERS x1 AND x2 OF “SUCCESSES” IN CORRESPONDING THE SAME PROCEDURE OF ENUMERATING THE (n1 +1)×(n2 +1) samples, WHERE 0 ≤ x1 ≤ n1 AND 0 ≤ x2 ≤ n2. The POSSIBLE differences, THIS TIME EXPLOITING THE INTEGRAL do- PURPOSE OF THE TEST IS TO DETERMINE WHETHER THE DIFFERENCE MAIN (0::1) OF THE π PARAMETER IN COMBINATION WITH AN ap- x1=n1 − x2=n2 RESULTS FROM ORDINARY RANDOM VARIATION PROPRIATE WEIGHTING function. OR IF IT IS PROBABILISTICALLY exceptional, GIVEN A probabil- Derivation OF THE EXACT TEST ITY threshold. Treatises AND TEXTBOOKS ON APPLIED statis- TICS REPORT A NUMBER OF TEST PROCEDURES USING SOME FORM OF Let R1 = (x1; n1) AND R2 = (x2; n2) BE THE RESULTS OF normal-based approximation, SUCH AS A Chi-squared test, TWO BINOMIAL observations, AND THEIR OBSERVED DIFFERENCE VARIOUS SORTS OF z (normal) AND t (Student’s) TESTS WITH OR dO = x1=n1 − x2=n2, WHERE R1 ∼ B(x1jn1; π1), R2 ∼ WITHOUT CONTINUITY correction, etc. -
6 Single Sample Methods for a Location Parameter
6 Single Sample Methods for a Location Parameter If there are serious departures from parametric test assumptions (e.g., normality or symmetry), nonparametric tests on a measure of central tendency (usually the median) are used. Recall: M is a median of a random variable X if P (X M) = P (X M) = :5. • ≤ ≥ The distribution of X is symmetric about c if P (X c x) = P (X c + x) for all x. • ≤ − ≥ For symmetric continuous distributions, the median M = the mean µ. Thus, all conclusions • about the median can also be applied to the mean. If X be a binomial random variable with parameters n and p (denoted X B(n; p)) then • n ∼ P (X = x) = px(1 p)n−x for x = 0; 1; : : : ; n x − n n! where = and k! = k(k 1)(k 2) 2 1: • x x!(n x)! − − ··· · − Tables exist for the cdf P (X x) for various choices of n and p. The probabilities and • cdf values are also easy to produce≤ using SAS or R. Thus, if X B(n; :5), we have • ∼ n P (X = x) = (:5)n x x n P (X x) = (:5)n ≤ k k X=0 P (X x) = P (X n x) because the B(n; :5) distribution is symmetric. ≤ ≥ − For sample sizes n > 20 and p = :5, a normal approximation (with continuity correction) • to the binomial probabilities is often used instead of binomial tables. (x :5) :5n { Calculate z = ± − : Use x+:5 when x < :5n and use x :5 when x > :5n. :5pn − { The value of z is compared to N(0; 1), the standard normal distribution. -
Tests of Hypotheses Using Statistics
Tests of Hypotheses Using Statistics Adam Massey¤and Steven J. Millery Mathematics Department Brown University Providence, RI 02912 Abstract We present the various methods of hypothesis testing that one typically encounters in a mathematical statistics course. The focus will be on conditions for using each test, the hypothesis tested by each test, and the appropriate (and inappropriate) ways of using each test. We conclude by summarizing the di®erent tests (what conditions must be met to use them, what the test statistic is, and what the critical region is). Contents 1 Types of Hypotheses and Test Statistics 2 1.1 Introduction . 2 1.2 Types of Hypotheses . 3 1.3 Types of Statistics . 3 2 z-Tests and t-Tests 5 2.1 Testing Means I: Large Sample Size or Known Variance . 5 2.2 Testing Means II: Small Sample Size and Unknown Variance . 9 3 Testing the Variance 12 4 Testing Proportions 13 4.1 Testing Proportions I: One Proportion . 13 4.2 Testing Proportions II: K Proportions . 15 4.3 Testing r £ c Contingency Tables . 17 4.4 Incomplete r £ c Contingency Tables Tables . 18 5 Normal Regression Analysis 19 6 Non-parametric Tests 21 6.1 Tests of Signs . 21 6.2 Tests of Ranked Signs . 22 6.3 Tests Based on Runs . 23 ¤E-mail: [email protected] yE-mail: [email protected] 1 7 Summary 26 7.1 z-tests . 26 7.2 t-tests . 27 7.3 Tests comparing means . 27 7.4 Variance Test . 28 7.5 Proportions . 28 7.6 Contingency Tables . -
A Flexible Statistical Power Analysis Program for the Social, Behavioral, and Biomedical Sciences
Running Head: G*Power 3 G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences (in press). Behavior Research Methods. Franz Faul Christian-Albrechts-Universität Kiel Kiel, Germany Edgar Erdfelder Universität Mannheim Mannheim, Germany Albert-Georg Lang and Axel Buchner Heinrich-Heine-Universität Düsseldorf Düsseldorf, Germany Please send correspondence to: Prof. Dr. Edgar Erdfelder Lehrstuhl für Psychologie III Universität Mannheim Schloss Ehrenhof Ost 255 D-68131 Mannheim, Germany Email: [email protected] Phone +49 621 / 181 – 2146 Fax: + 49 621 / 181 - 3997 G*Power 3 (BSC702) Page 2 Abstract G*Power (Erdfelder, Faul, & Buchner, Behavior Research Methods, Instruments, & Computers, 1996) was designed as a general stand-alone power analysis program for statistical tests commonly used in social and behavioral research. G*Power 3 is a major extension of, and improvement over, the previous versions. It runs on widely used computer platforms (Windows XP, Windows Vista, Mac OS X 10.4) and covers many different statistical tests of the t-, F-, and !2-test families. In addition, it includes power analyses for z tests and some exact tests. G*Power 3 provides improved effect size calculators and graphic options, it supports both a distribution-based and a design-based input mode, and it offers all types of power analyses users might be interested in. Like its predecessors, G*Power 3 is free. G*Power 3 (BSC702) Page 3 G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences Statistics textbooks in the social, behavioral, and biomedical sciences typically stress the importance of power analyses. -
Week 10: Chapter 10
EEOS 601 UMASS/Online Introduction to Probability & Applied Statistics Handout 13, Week 10 Tu 8/2/11-M 8/8/11 Revised: 3/20/11 WEEK 10: CHAPTER 10 TABLE OF CONTENTS Page: List of Figures. ................................................................................... 2 List of Tables. .................................................................................... 2 List of m.files. .................................................................................... 2 Assignment.. 3 Required reading. 3 Understanding by Design Templates. .................................................................. 4 Understanding By Design Stage 1 — Desired Results...................................................... 4 Understanding by Design Stage 2 — Assessment Evidence Week 10 Tu 8/2-8/8................................. 4 Introduction. ..................................................................................... 5 Theorems and definitions. ........................................................................... 7 Theorem 10.2.1. 7 Theorem 10.3.1. 7 Theorem 10.4.1. 7 Theorem 10.5.1. 8 Statistical Tests.. 9 Fisher’s hypergeometric test. ................................................................. 9 Fisher’s test as an exact test for tests of homogeneity and independence. ....................... 10 Fisher’s test and Matlab. 11 What is a test of homogeneity?. .............................................................. 11 Sampling schemes producing contingency tables. ................................................ 11 Case