HO Hartley Publications by Year

Total Page:16

File Type:pdf, Size:1020Kb

HO Hartley Publications by Year APPENDIX H.O. Hartley Publications by Year (1935-1980) BOOKS Pearson, ES; Hartley, HO. Biomtrika Tables for Statisticians, Vol. I. Biometrika Publications, Cambridge University Press, Bentley House, London, 1954 Greenwood, JA; Hartley, HO. Guide to Tables in Mathematical Statistics, Princeton University Press, Princeton, New Jersey, 1961 Pearson, ES; Hartley, HO. Biomtrika Tables for Statisticians, Vol. II. Biometrika Publications, Cambridge University Press, Bentley House, London, 1972 PEER- REVIEWED PUBLISHED MANUSCRIPTS 1935 *Hirshchfeld, HO. A Connection between Correlation and Contingency. Proceedings of the Cambridge Philosophical Society (Math. Proc.) 31: 520-524 1936 *Hirschfeld, HO. A Generalization of Picard’s Method of Successive Approximation. Proceedings of the Cambridge Philosophical Society 32: 86-95 *Hirschfeld, HO. Continuation of Differentiable Functions through the Plane. The Quarterly Journal of Mathematics, Oxford Series, 7: 1-15 Wishart, J; *Hirschfeld, HO. A Theorem Concerning the Distribution of Joins between Line Segments. Journal of the London Mathematical Society, 11: 227-235 1937 *Hirschfeld, HO. The Distribution of the Ratio of Covariance Estimates in Two Samples Drawn from Normal Bivariate Populations. Biometrika 29: 65-79 *Manuscripts dated from 1935 to 1937 are listed under born name of Hirschfeld, Hermann Otto. Manuscripts dated from 1938 -1980 are listed under changed name of Hartley, Herman Otto. 1938 Hunter, H; Hartley, HO. Relation of Ear Survival to the Nitrogen Content of Certain Varieties of Barley – With a Statistical Study. Journal of Agricultural Science 28: 472-502 Hartley, HO. Studentization and Large Sample Theory. Supplement to the Journal of the Royal Statistical Society 5: 80-88 1940 Hartley, HO. Testing the Homogeneity of a Set of Variances. Biometrika 31: 249-255 1941 Comrie, LJ; Hartley, HO. Table of Lagrangian Coefficients for Harmonic Interpolation in Certain Tables of Percentage Points. Biometrika 32: 183-186 Thompson, CM; Pearson, ES; Comrie, LJ; Hartley, HO. Tables of Percentage Points of the Incomplete Beta- Function. Biometrika 32: 151-181 1942 Hartley, HO. The Range in Random Samples. Biometrika 32: 334-348 Hartley, HO; Pearson, ES. The Probability Integral of the Range in Samples of n Observations from a Normal Population. Biometrika 32: 301-310 1943 Pearson, ES; Hartley, HO. Tables of the Probability Integral of the Studentized Range. Biometrika 33:89-99 1944 Hartley, HO. Studentization or the Elimination of the Standard Deviation of the Parent Population from the Random Sample Distribution of Statistics. Biometrika 33:173-180 1945 Hartley, HO. Note on the Calculation of the Distribution of the Estimate of Mean Deviation in Normal Samples. Biometrika 33: 257-258 Hartley, HO; Goodwin,HJ. Tables of the Probability Integral and Percentage Points of the Mean Deviation in Samples from Normal Populations. Biometrika 33: 252-265 1946 Hartley, HO. The Application of Some Commercial Calculating Machines to Certain Statistical Calculations. Journal of the Royal Statistical Society, Series B, 8:154-183 Hartley, HO. Tables for Testing the Homogeneity of Estimated Variances. Biometrika 33: 296-304 1947 Hartley, HO; Khamis, SH. A Numerical Solution of the Problem of Moments. Biometrika 34: 340-351 1948 Hartley, HO. The Estimation of Non-Linear Parameters by Internal Least Squares. Biometrika 35:32-45 Smith, CAB; Hartley, HO. The Construction of Youden Squares. Journal of the Royal Statistical Society, Series B, 10: 262-263 Hartley, HO; Approximation Errors in Distributions of Independent Variates. Biometrika 35:417-418 1949 Hartley, HO. Tests of Significance in Harmonic Analysis. Biometrika 36: 194-201 1950 Hartley, HO. A Simplified Form of Sheppard’s Correction Formulae. Biometrika 37: 145-148 Hartley, HO. The Use of Range in Analysis of Variance. Biometrika 37: 271-280 Hartley, HO. The Maximum F-Ratio as a Short-Cut Test for Heterogeneity of Variance. Biometrika 37: 308- 312 Hartley, HO; Pearson, ES. Tables of the χ2-Integral and of the Cumulative Poisson Distribution. Biometrika 37: 313-325 Hartley, HO; Pearson, ES. Table of the Probability Integral of the t- Distribution. Biometrika 37: 168-172 1951 Pearson, ES; Hartley, HO. Charts of the Power Function for Analysis of Variance Tests, Derived from the Non-Central F-Distribution. Biometrika 38:112-130 Hartley, HO. The Fitting of Polynomials to Equidistant Data with Missing Values. Biometrika 38:410-413 Hartley, HO. A Chart for the Incomplete Beta-Function and the Cumulative Binomial Distribution. Biometrika 38:423-426 Hartley, HO; Stones, HH; Lawton, FE; Bransby, ER. Time of Eruption of Permanent Teeth and Time of Shedding of Deciduous Teeth. British Dental Journal 90:1-7 Hartley, HO; Pearson, ES. Moment Constants for the Distribution of Range in Normal Samples. Biometrika 38: 463-464 1952 Hartley, HO. Second Order Autoregressive Schemes with Time-Trending Coefficients. Journal of the Royal Statistical Society, Series B, 14: 229-233 Hartley, HO; Pearson, ES. Tables for Numerical Integration at Non-Equidistant Argument Steps. Mathematical Proceedings of the Cambridge Mathematical Society 48: 436-444 1953 Hartley, HO; Shrikande, SS; Taylor, WB. A Note on Incomplete Designs with Row Balance. The Annals of Mathematical Statistics 24: 123-126 Hartley, HO; Keen, J; Denys, JP. Some Theoretical Aspects of Estimating Variability from the Differences between Successive Readings. Applied Statistics II 13: 20-23 1954 Hartley, HO; David, HA. Universal Bounds for Mean Range and Extreme Observation. Annals of Mathematical Statistics 25: 85-99 David, HA; Hartley, HO; Pearson, ES. The Distribution of the Ratio, in a Single Normal Sample, of Range to Standard Deviation. Biometrika 41:482-493 Fieller, EC; Hartley, HO. Sampling with Control Variables. Biometrika 41:494-501 1955 Hartley, HO. Some Recent Developments in Analysis of Variance. Communications on Pure and Applied Mathematics 8: 47-72 1956 Bozivich, H; Bancroft, TA; Hartley, HO. Power of Analysis of Variance Test Procedures for Certain Incompletely Specified Models, I. Annals of Mathematical Statistics 27: 1017-1043 Hartley, HO. A Plan for Programming Analysis of Variance for General Purpose Computers. Biometrics 12:110-122 1957 Fieller, EC; Hartley, HO; Pearson, ES. Tests for Rank Correlation Coefficients, I. Biometrika 44: 470-481 1958 Hartley, HO. Maximum Likelihood Estimation from Incomplete Data. Biometrics 14: 174-194 Carter, HO; Hartley, HO. A Variance Formula for Marginal Productivity Estimates Using the Cobb-Douglas Function. Econometrica 26: 306-313 Goodman, LA; Hartley, HO. The Precision of Unbiased Ratio-Type Estimators. Journal of the American Statistical Association 53: 491-508 Hartley, HO; Loftsgard, LD. Linear Programming with Variable Constraints. Iowa State Journal of Sciences 33: 161-172 1959 Hartley, HO. Smallest Composite Designs for Quadratic Response Surfaces. Biometrics 15: 610-624 Hartley, HO. The Efficiency of Internal Regression for the Fitting of the Exponential Regression. Biometrika 46: 293-295 1960 Bryant, EC; Hartley, HO; Jessen, RJ. Design and Estimation in Two-Way Stratification. Journal of the American Statistical Association 55:105-124 1961 Hartley, HO. Nonlinear-Programming by the Simplex-Method. Econometrica 29: 223-237 Hartley, HO. The Modified Gauss-Newton Method for Fitting of Non-Linear Regression Functions by Least Squares. Technometrics 3: 269-280 1962 Hartley, HO; Rao, JNK. Sampling with Unequal Probabilities and without Replacement, Annals of Mathematical Statistics 33: 350-374 Hartley, HO; Rao, JNK; Cochran, WG. On a Simple Procedure of Unequal Probability Sampling without Replacement. Journal of the Royal Statistical Society, Series B, 24: 487-491 1963 Hartley, HO; Hocking, RR. Convex-Programming by Tangential Approximation. Management Science 9: 600-612 Hartley, HO; Harris, DL. Monte Carlo Computations in Normal Correlation Problems. Journal of the Association of Computing Machinery 10: 302-306 1964 Hartley, HO. Exact Confidence Regions for Parameters in Non-Linear Regression Laws. Biometrika 51:347- 353 1965 Hartley, HO; Booker, A. Nonlinear Least Squares Estimation. Annals of Mathematical Statistics 36: 638-650 1966 Hartley, HO. Systematic Sampling with Unequal Probability and Without Replacement. Journal of the American Statistical Association 61: 739-748 Hartley, HO; Worthan, AW. A Statistical Theory for PERT Critical Path Analysis. Management Sciences, Series B, 12: 469-491 . 1967 Hartley, HO. Expectations, Variances, and Covariances of ANOVA Mean Squares by Synthesis. Biometrics 23: 104-114 Hartley, HO; Rao, JNK. Maximum-Likelihood Estimation for Mixed Analysis of Variance Model. Biometrika 54: 93-108: Freund, RJ; Hartley, HO. A Procedure for Automatic Data Editing. Journal of the American Statistical Association 62: 341-352 Hartley, HO; Chakrabarty, RP. Evaluation of Approximate Variance Formulas in Sampling with Unequal Probabilities and without Replacement. Sankya: The Indian Journal of Statistics, Series B, 29: 201-208 Hartley, HO; Hocking, RR; Cooke, WP. Least Squares Fit of Definite Quadratic Forms by Convex Programming. Management Sciences 13: 913-925. 1968 Broemeling, LD; Hartley, HO. Investigations of Optimality of a Confidence Region for Parameters of a Non- Linear Regression Model. Annals of the Institute of Statistical Mathematics 20: 263-269 Hartley, HO; Rao, JNK. A New Estimation Theory for Sample Surveys. Biometrika 55: 547-557 Smith, WB; Hartley, HO. A Note on Correlation of Ranges in Correlated Normal Samples.
Recommended publications
  • A Simple but Accurate Excel User-Defined Function to Calculate Studentized Range Quantiles for Tukey Tests
    A Simple but Accurate Excel United States Department of User-Defined Function to Agriculture Calculate Studentized Range Agricultural Quantiles for Tukey Tests Research Service K. Thomas Klasson Southern Regional Research Center Technical Report June 2019 Revised February 2020 The Agricultural Research Service (ARS) is the U.S. Department of Agriculture's chief scientific in-house research agency. Our job is finding solutions to agricultural problems that affect Americans every day from field to table. ARS conducts research to develop and transfer solutions to agricultural problems of high national priority and provide information access and dissemination of its research results. The U.S. Department of Agriculture (USDA) prohibits discrimination in all its programs and activities on the basis of race, color, national origin, age, disability, and where applicable, sex, marital status, familial status, parental status, religion, sexual orientation, genetic information, political beliefs, reprisal, or because all or part of an individual's income is derived from any public assistance program. (Not all prohibited bases apply to all programs.) Persons with disabilities who require alternative means for communication of program information (Braille, large print, audiotape, etc.) should contact USDA's TARGET Center at (202) 720-2600 (voice and TDD). To file a complaint of discrimination, write to USDA, Director, Office of Civil Rights, 1400 Independence Avenue, S.W., Washington, D.C. 20250-9410, or call (800) 795-3272 (voice) or (202) 720-6382 (TDD). USDA is an equal opportunity provider and employer. K. Thomas Klasson is a Supervisory Chemical Engineer at USDA-ARS, Southern Regional Research Center, 1100 Robert E. Lee Boulevard, New Orleans, LA 70124; email: [email protected] A Simple but Accurate Excel User-Defined Function to Calculate Studentized Range Quantiles for Tukey Tests K.
    [Show full text]
  • Studentized Range Upper Quantiles
    A Table of Upper Quantile Points of the Studentized Range Distribution This is a table of upper quantile points of the studentized range distribution, values that are required by several statistical techniques including the Tukey wsd and the Newman-Keuls multiple comparison procedures. The table entries are given to four significant digits, in the style of the classic table for this distribution (Harter, 1960; Harter & Clemm, 1959). 2 Suppose that X(1) and X(r) are the smallest and largest order statistics in r independent N(µ, σ ) random variables. That is, X(1) and X(r) are the minimum and maximum values in a simple random sample of size r from the normal distribution with mean µ and variance σ2. The (externally) studentized range is a variable of the form X − X Q = (r) (1) S 2 2 2 where νS /σ is a χ (ν) random variable that is independent of X(r) − X(1). The p-th quantile qp(r; ν)ofthe distribution of Q satisfies Pr(Q ≤ qp(r; ν)) = p; where 0 <p<1: That is, the area to the right of qp(r; ν) under the density function of Q is 1 − p. This table includes 4944 values of qp(r; ν), at all combinations of the following parameters: • p =0:50; 0:75; 0:90; 0:95; 0:975; 0:99; 0:995; 0:999 • r = 2(1)20; 30; 40(20)100 • ν = 1(1)20; 24; 30; 40; 60; 120; ∞ except that no values are provided for ν =1atp =0:50 or p =0:75.
    [Show full text]
  • Application of Range in the Overall Analysis of Variance
    TOE APPLICATION OF RANGE IN TOE OTERALL ANALYSIS OF VARIANCE lor BARREL LEE EKLUND B, S,, Kansas State Qilvtersltj, I96I1 A MASTER'S REPORT submitted in partial fulfillment of the requirements for the degree MASTER OF SCIENCE Department of Statistics KANSAS STATE UNIVERSITT Manhattan, Kansas 1966 Approved by: Jig^^^&e^;css^}^Li<<>:<^ LP M^ ii r y. TABLE OF CONTENTS INTRODUCTION 1 HISTORICAL REVIEW AND RATIONALE 1 Developments in the use of Range • • 1 ^proximation to the Distribution of Mean Range. ••• 2 Distribution of the Range Ratio. ....•..•••.••.•. U niscussion of Sanple Range •• .......... U COMPLETELY RANDOMIZED DE?IGN 5 Theoretical Basis. • ....•.•... $ Illustration of Procedure 6 RANDOMIZED COMPLETE BLOCK DESIGN 7 Distaribution Theory for the Randomized Block Analysis by Range . 7 'Studentized' Range Test as a Substitute for the F-test 8 Illustration of Procedure. ..•.......•....•••. 9 COMPLETELY RANDOMIZED DESIGN WITH CELL REPLICATION AND FACTORIAL ARRANGEMENT OF TREATI-IENTS 11 P^ed Model 12 Random Ifodel 13 Illustration of Procedure , 11^ RANDOMIZED CCMPLE'lTi; BLOCK DESIGN WITH FACTORIAL ARRANGEMENT OF TREATIIEOTS I7 Theoretical Basis. I7 Illustration of Procedure. ............ I9 SPLIT-PLOT DESIGN 21 Hiaeoretical Basis 21 Illustration of Procedure , 23 COMPLETKLY RANDOMIZED DESIGN WITH UNEQUAL Cmi. HffiQUENCIES 26 iii MULTIPLE COMPARISONS 28 Multiple Q-test 28 Stepwise Reduction of the q-test • .....30 POWER OF THE RANQE TEST IN EIEMENTARY DESIGNS .30 Random Model. .•• ••••••• 31 Fixed Model • 33 SUI-IMARY 33 ACKNCKLEDGEMENT 3$ REFERENCES • 36 APPENDIX ••• ..*37 ) THE APPLICAnON OF RANGE IN THE OVERALL ANALYSIS OF VARIANCE INTRODUCTION One of the best known estimators of the variation within a sample is the sajiple range.
    [Show full text]
  • The Combination of Statistical Tests of Significance Wendell Carl Smith Iowa State University
    Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1974 The combination of statistical tests of significance Wendell Carl Smith Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Statistics and Probability Commons Recommended Citation Smith, Wendell Carl, "The ombc ination of statistical tests of significance " (1974). Retrospective Theses and Dissertations. 5120. https://lib.dr.iastate.edu/rtd/5120 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. INFORMATION TO USERS This material was produced from a microfilm copy of the original document. While the most advanced technological means to photograph and reproduce this document have been used, the quality is heavily dependent upon the quality of the original submitted. The following explanation of techniques is provided to help you understand markings or patterns which may appear on this reproduction. 1. The sign or "target" for pages apparently lacking from the document photographed is "Missing Page(s)". If it was possible to obtain the missing page(s) or section, they are spliced into the film along with adjacent pages. This may have necessitated cutting thru an image and duplicating adjacent pages to insure you complete continuity. 2. When an image on the film is obliterated with a large round black mark, it is an indication that the photographer suspected that the copy may have moved during exposure and thus cause a blurred image.
    [Show full text]
  • 773593683.Pdf
    LAKE AREA CHANGE IN ALASKAN NATIONAL WILDLIFE REFUGES: MAGNITUDE, MECHANISMS, AND HETEROGENEITY A DISSERTATION Presented to the Faculty of the University of Alaska Fairbanks In Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY By Jennifer Roach, B.S. Fairbanks, Alaska December 2011 iii Abstract The objective of this dissertation was to estimate the magnitude and mechanisms of lake area change in Alaskan National Wildlife Refuges. An efficient and objective approach to classifying lake area from Landsat imagery was developed, tested, and used to estimate lake area trends at multiple spatial and temporal scales for ~23,000 lakes in ten study areas. Seven study areas had long-term declines in lake area and five study areas had recent declines. The mean rate of change across study areas was -1.07% per year for the long-term records and -0.80% per year for the recent records. The presence of net declines in lake area suggests that, while there was substantial among-lake heterogeneity in trends at scales of 3-22 km a dynamic equilibrium in lake area may not be present. Net declines in lake area are consistent with increases in length of the unfrozen season, evapotranspiration, and vegetation expansion. A field comparison of paired decreasing and non-decreasing lakes identified terrestrialization (i.e., expansion of floating mats into open water with a potential trajectory towards peatland development) as the mechanism for lake area reduction in shallow lakes and thermokarst as the mechanism for non-decreasing lake area in deeper lakes. Consistent with this, study areas with non-decreasing trends tended to be associated with fine-grained soils that tend to be more susceptible to thermokarst due to their higher ice content and a larger percentage of lakes in zones with thermokarst features compared to study areas with decreasing trends.
    [Show full text]
  • STAT 5200 Handout #7A Contrasts & Post Hoc Means Comparisons
    STAT 5200 Handout #7a Contrasts & Post hoc Means Comparisons (Ch. 4-5) Recall CRD means and effects models: 2 Yij = µi + ij i = 1; : : : ; g ; j = 1; : : : ; n ; ij's iid N(0; σ ) = µ + αi + ij • If we reject H0 : µ1 = ::: = µg (based on FT rt), it's natural to look more carefully at why • How are µi's not equal? { We usually make pairwise comparisons: { This involves two issues: ∗ Testing \contrasts" ∗ Dealing with multiple hypothesis Contrasts: • A linear combination of parameters (like µi's or αi's) g g X X = wiµi or = wiαi i=1 i=1 where g X wi = 0 i=1 This definition leads to some nice statistical properties • In a CRD (one-way ANOVA), all contrasts are \estimable": (i.e., they have unique least squares estimates and SE's) g ^ X Pg = wiµ^i = i=1 wiα^i i=1 • For means model parameterization (not so clean for effects model): v g q u ^ ^ u 2 X 2 SE of = V ar[ ] = tσ^ wi =ni i=1 • We can use these to get 95% C.I. for : ^ ^ ± (t:025;N−g) × SE of • Equivalently, test H0: = 0 using 2 32 ^ ^ or, equivalently 4 5 SE of ^ SE of ^ • We look at a different in each pairwise comparison of treatments { but does not need to be a pairwise comparison Multiple Hypothesis Testing (as in testing all possible pairwise treatment comparisons): Recall in significance testing: • Type I error: Type I error rate: • Type II error: Type II error rate: • Power: How to set tolerance for a Type I error when testing all K possible pairwise treatment comparisons? • When we test H0 at level α, this is an error rate • If we test KH0's (all true), each at level α = 0:05, how likely are we to reject any just by chance? P freject at least one H0 j all trueg = 1 − P freject none j all trueg = 1 − P fdon't reject #1 and don't reject #2 and ::: j all trueg K = 1 − (P fdon't reject H0 j H0 true) = 1 − (1 − α)K ≈ So testing all H0's at α = 0:05 can make at least one Type I error quite likely! • With multiple H0's, we need to consider meaningful error rates • Type I error rates of major interest: (for a \family" of K nulls H01;H02;:::;H0K ) 1.
    [Show full text]
  • Chapter 12 Multiple Comparisons Among
    CHAPTER 12 MULTIPLE COMPARISONS AMONG TREATMENT MEANS OBJECTIVES To extend the analysis of variance by examining ways of making comparisons within a set of means. CONTENTS 12.1 ERROR RATES 12.2 MULTIPLE COMPARISONS IN A SIMPLE EXPERIMENT ON MORPHINE TOLERANCE 12.3 A PRIORI COMPARISONS 12.4 POST HOC COMPARISONS 12.5 TUKEY’S TEST 12.6 THE RYAN PROCEDURE (REGEQ) 12.7 THE SCHEFFÉ TEST 12.8 DUNNETT’S TEST FOR COMPARING ALL TREATMENTS WITH A CONTROL 12.9 COMPARIOSN OF DUNNETT’S TEST AND THE BONFERRONI t 12.10 COMPARISON OF THE ALTERNATIVE PROCEDURES 12.11 WHICH TEST? 12.12 COMPUTER SOLUTIONS 12.13 TREND ANALYSIS A significant F in an analysis of variance is simply an indication that not all the population means are equal. It does not tell us which means are different from which other means. As a result, the overall analysis of variance often raises more questions than it answers. We now face the problem of examining differences among individual means, or sets of means, for the purpose of isolating significant differences or testing specific hypotheses. We want to be able to make statements of the form 1 2 3 , and 45 , but the first three means are different from the last two, and all of them are different from 6 . Many different techniques for making comparisons among means are available; here we will consider the most common and useful ones. A thorough discussion of this topic can be found in Miller (1981), and in Hochberg and Tamhane (1987), and Toothaker (1991). The papers by Games (1978a, 1978b) are also helpful, as is the paper by Games and Howell (1976) on the treatment of unequal sample sizes.
    [Show full text]
  • Externally Studentized Normal Midrange Distribution Distribuição Da Midrange Estudentizada Externamente
    Ciência e Agrotecnologia 41(4):378-389, Jul/Aug. 2017 http://dx.doi.org/10.1590/1413-70542017414047716 Externally studentized normal midrange distribution Distribuição da midrange estudentizada externamente Ben Dêivide de Oliveira Batista1*, Daniel Furtado Ferreira2, Lucas Monteiro Chaves2 1Universidade Federal de São João del-Rei/UFSJ, Departamento de Matemática e Estatística/DEMAT, São João del-Rei, MG, Brasil 2Universidade Federal de Lavras/UFLA, Departamento de Estatística/DES, Lavras, MG, Brasil *Corresponding author: [email protected] Received in December 15, 2016 and approved in February 15, 2017 ABSTRACT The distribution of externally studentized midrange was created based on the original studentization procedures of Student and was inspired in the distribution of the externally studentized range. The large use of the externally studentized range in multiple comparisons was also a motivation for developing this new distribution. This work aimed to derive analytic equations to distribution of the externally studentized midrange, obtaining the cumulative distribution, probability density and quantile functions and generating random values. This is a new distribution that the authors could not find any report in the literature. A second objective was to build an R package for obtaining numerically the probability density, cumulative distribution and quantile functions and make it available to the scientific community. The algorithms were proposed and implemented using Gauss-Legendre quadrature and the Newton-Raphson method in R software, resulting in the SMR package, available for download in the CRAN site. The implemented routines showed high accuracy proved by using Monte Carlo simulations and by comparing results with different number of quadrature points. Regarding to the precision to obtain the quantiles for cases where the degrees of freedom are close to 1 and the percentiles are close to 100%, it is recommended to use more than 64 quadrature points.
    [Show full text]
  • Specific Differences
    Specific Differences Lukas Meier, Seminar für Statistik Problem with Global 퐹-test . Problem: Global 퐹-test (aka omnibus 푭-test) is very unspecific. Typically: Want a more precise answer (or have a more specific question) on how the group means differ. Examples . Compare new treatments with control treatment (reference treatment). Do pairwise comparisons between all treatments. …. A specific question can typically be formulated as an appropriate contrast. 1 Contrasts: Simple Example . Want to compare group 2 with group 1 (don’t care about the remaining groups for the moment). 퐻0: 휇1 = 휇2 vs. 퐻퐴: 휇1 ≠ 휇2. Equivalently: 퐻0: 휇1 − 휇2 = 0 vs. 퐻퐴: 휇1 − 휇2 ≠ 0. The corresponding contrast would be 푐 = 1, −1, 0, 0, … , 0 . A contrast 푐 ∈ ℝ푔 is a vector that encodes the null hypothesis in the sense that 푔 퐻0: 푐푖 ⋅ 휇푖 = 0 푖=1 . A contrast is nothing else than an encoding of your research question. 2 Contrasts: Formal Definition . Formally, a contrast is nothing else than a vector 푔 푐 = (푐1, 푐2, … , 푐푔) ∈ ℝ 푔 with the constraint that 푖=1 푐푖 = 0. The constraint reads: “contrast coefficients add to zero”. The side constraint ensures that the contrast is about differences between group means and not about the overall level of our response. Mathematically speaking, 푐 is orthogonal to 1, 1, … , 1 or 1/푔, 1/푔, … , 1/푔 which is the overall mean. Means: Contrasts don’t care about the overall mean. 3 More Examples using Meat Storage Data . Treatments were 1) Commercial plastic wrap (ambient air) Current techniques (control groups) 2) Vacuum package 3) 1% CO, 40% O2, 59% N New techniques 4) 100% CO2 .
    [Show full text]
  • Probability Distributions and Density Functions
    Title stata.com functions — Functions Description Acknowledgments References Also see Description This entry describes the functions allowed by Stata. For information on Mata functions, see [M-4] intro. A quick note about missing values: Stata denotes a numeric missing value by ., .a, .b, ::: , or .z. A string missing value is denoted by "" (the empty string). Here any one of these may be referred to by missing. If a numeric value x is missing, then x ≥ . is true. If a numeric value x is not missing, then x < . is true. Functions are listed under the following headings: Mathematical functions Probability distributions and density functions Random-number functions String functions Programming functions Date and time functions Selecting time spans Matrix functions returning a matrix Matrix functions returning a scalar Mathematical functions abs(x) Domain: −8e+307 to 8e+307 Range: 0 to 8e+307 Description: returns the absolute value of x. acos(x) Domain: −1 to 1 Range: 0 to π Description: returns the radian value of the arccosine of x. acosh(x) Domain: 1 to 8.9e+307 Range: 0 to 709.77 p Description: returns the inverse hyperbolic cosine of x, acosh(x) = ln(x + x2 − 1). asin(x) Domain: −1 to 1 Range: −π=2 to π=2 Description: returns the radian value of the arcsine of x. asinh(x) Domain: −8.9e+307 to 8.9e+307 Range: −709.77 to 709.77 p Description: returns the inverse hyperbolic sine of x, asinh(x) = ln(x + x2 + 1). 1 2 functions — Functions atan(x) Domain: −8e+307 to 8e+307 Range: −π=2 to π=2 Description: returns the radian value of the arctangent of x.
    [Show full text]
  • QXLA: Adding Upper Quantiles for the Studentized Range to Excel for Multiple Comparison Procedures
    JSS Journal of Statistical Software June 2018, Volume 85, Code Snippet 1. doi: 10.18637/jss.v085.c01 QXLA: Adding Upper Quantiles for the Studentized Range to Excel for Multiple Comparison Procedures K. Thomas Klasson United States Department of Agriculture Abstract Microsoft Excel has some functionality in terms of basic statistics; however it lacks distribution functions built around the studentized range (Q). The developed Excel add- in introduces two new user-defined functions, QDISTG and QINVG, based on the studentized range Q-distribution that expands the functionality of Excel for statistical analysis. A workbook example, demonstrating the Tukey, S-N-K, and REGWQ tests, has also been included. Compared with other options available, the method is fast with low error rates. Keywords: Microsoft Excel, VisualBasics, VBA, add-in, studentized range, Q-distribution. 1. Introduction Researchers in most fields of science are often faced with comparing means obtained with various treatments. The statistical analysis using multiple comparison procedures (MCPs) is often carried out by statistical software packages that are less suitable for data storage and manipulation. While Microsoft Excel offers excellent data storage and manipulation, it provides few built-in methods for statistical data analysis. Excel’s Analysis ToolPak add-in provides basic analysis of variance (single factor and two-factor) and also provides t-tests for two sample means. The availability of Excel functions such as FDIST, FINV, TDIST, and TINV for the F - and t-distributions allows for some capability to conduct simple multiple comparison procedures such as Fisher’s least significant difference test. However, the lack of Excel support for the studentized range (Q) distribution does not allow for the Tukey honest significant difference, Student-Newman-Keuls (S-N-K), or Ryan-Einot-Gabriel-Welsch Q (REGWQ) tests to be carried out.
    [Show full text]
  • Quantiles from the Maximum Studentized Range Distribution
    QUANTILES FROM THE MAXIMUM STUDENTIZED RANGE DISTRIBUTION Daniel Furtado FERREIRA1 Clarice Garcia Borges DEMÉTRIO2 Bryan Frederick John MANLY3 Amauri de Almeida MACHADO4 ° ABSTRACT: The Copenhaver and Holland (1988) algorithm for calculating quantiles and the distribution function of the maximum of c statistics having studentized range distributions of r sample means obtained from random a sample of size n from normal homocedastic distributions was adapted and implemented in Pascal. The algorithm uses Gauss-Legendre quadrature to obtain the distribution function and uses the secant method to calculate the 100p% quantiles from that distribution. The main advantage of the implemented algorithm is that it is not limited to the range of quantiles from 90% to 99%, and it is more accurate than the iterative procedure proposed by Lund and Lund (1983). When c = 1 the algorithm supplies the cumulative distribution function and the quantiles of the studentized range distribution, except for the particular case where the number of degrees of freedom is v=1. In general, the accuracy of the algorithm decreases as r increases, as v decreases and as p approaches 1. Also r and v have a larger effect on accuracy. Differences among the results from Tukey and maximum studentized range quantiles were shown in a real example. These differences were due to the guarantee of the overall protection for the global confidence coefficient only in the maximum studentized range distribution. ° KEYWORDS: Studentized range; quantiles 1 Introduction The studentized range distribution is applied in some widely used multiple comparisons tests involving sample means from normal homocedastic distributions, a subject discussed in many articles since the 1950s (Tukey, 1952; Keuls, 1952; Hochberg and Tamhane, 1987).
    [Show full text]