A Chronicle of Permutation Statistical Methods

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The focus of this book is on the birth and historical development of permutation statistical methods from the early 1920s to the near present. Beginning with the seminal contributions of R.A. Fisher, E.J.G. Pitman, and others in the 1920s and 1930s, permutation statistical methods were initially introduced to validate the assumptions of classical statistical methods.

Permutation methods have advantages over classical methods in that they are optimal for small data sets and non-random samples, are data-dependent, and are free of distributional assumptions. Permutation probability values may be exact, or estimated via moment- or resampling-approximation procedures. Because permutation methods are inherently computationally-intensive, the evolution of computers and computing technology that made modern permutation methods possible accompanies the historical narrative.

Permutation analogs of many well-known statistical tests are presented in a historical context, including multiple correlation and regression, analysis of variance, contingency table analysis, and measures of association and agreement. A non-mathematical approach makes the text accessible to readers of all levels.


Kenneth J. Berry is Professor of Sociology at Colorado State University.

Janis E. Johnston is a Social Science Policy Analyst with the United States government in Washington, D.C.

Paul W. Mielke, Jr. is Professor Emeritus of Statistics at Colorado State University and Fellow of the American Statistical Association.


Preface.- 1.Introduction.- 2.19201939.- 2.1.Overview of Chapter 2.- 2.2.NeymanFisherGeary and the Beginning.- 2.3.Fisher and the Variance-ratio Statistic.- 2.4.EdenYates and Non-normal Data.- 2.5.Fisher and 2 by 2 Contingency Tables.- 2.6 Yates and the Chi-squared Test for Small Samples.- 2.7.Irwin and Fourfold Contingency Tables.- 2.8.The Rothamsted Manorial Estate.- 2.9.Fisher and the Analysis of Darwin's Zea mays Data.- 2.10.Fisher and the Coefficient of Racial Likeness.- 2.11.HotellingPabst and Simple Bivariate Correlation.- 2.12.Friedman and Analysis of Variance for Ranks.- 2.13.Welch's Randomized Blocks and Latin Squares.- 2.14.Egon Pearson on Randomization.- 2.15.Pitman and Three Seminal Articles.- 2.16.Welch and the Correlation Ratio.- 2.17.Olds and Rank-order Correlation.- 2.18.Kendall and Rank Correlation.- 2.19.McCarthy and Randomized Blocks.- 2.20.Computing and Calculators.- 2.21.Looking Ahead.- 3.19401959.- 3.1.Overview of Chapter 3.- 3.2.Development of Computing.- 3.3.KendallBabington Smith and Paired Comparisons.- 3.4.Dixon and a Two-sample Rank Test.- 3.5.Swed-Eisenhart and Tables for the Runs Test.- 3.6.Scheff´e and Non-parametric Statistical Inference.- 3.7.WaldWolfowitz and Serial Correlation.- 3.8.Mann and a Test of Randomness Against Trend.- 3.9.Barnard and 2 by 2 Contingency Tables.- 3.10.Wilcoxon and the Two-sample Rank-sum Test.- 3.11.Festinger and the Two-sample Rank-sum Test.- 3.12.MannWhitney and a Two-sample Rank-sum Test.- 3.13.Whitfield and a Measure of Ranked Correlation.- 3.14.OlmsteadTukey and the Quadrant-sum Test.- 3.15.HaldaneSmith and a Test for Birth-order Effects.- 3.16.Finney and the FisherYates Test for 2 by 2 Tables.- 3.17.LehmannStein and Non-parametric Tests.- 3.18 Rank-order Statistics.- 3.19.van der Reyden and a Two-sample Rank-sum Test.-3.20.White and Tables for the Rank-sum Test.- 3.21.Other Results for the Two-sample Rank-sum Test.- 3.22.DavidKendallStuart and Rank-order Correlation.- 3.23.FreemanHalton and an Exact Test of Contingency.- 3.24.KruskalWallis and the C-sample Rank-sum Test.- 3.25.BoxAndersen and Permutation Theory.- 3.26.Leslie and Small Contingency Tables.- 3.27.A Two-sample Rank Test for Dispersion.- 3.28.Dwass and Modified Randomization Tests.- 3.29.Looking Ahead.- 4.19601979.- 4.1.Overview of Chapter 4.- 4.2.Development of Computing.- 4.3 Permutation Algorithms and Programs.- 4.4.Ghent and the FisherYates Exact Test.- 4.5.Programs for Contingency Table Analysis.- 4.6.SiegelTukey and Tables for the Test of Variability.- 4.7 .Other Tables of Critical Values.- 4.8.Edgington and Randomization Tests.- 4.9.The Matrix Occupancy Problem.- 4.10.Kempthorne and Experimental Inference.- 4.11.BakerCollier and Permutation F Tests 4.12.Permutation Tests in the 1970s.- 4.13.Feinstein and Randomization.- 4.14.The MannWhitney, Pitman, and Cochran Tests.- 4.15.MielkeBerryJohnson and MRPP.- 4.16.Determining the Number of Contingency Tables.- 4.17.Soms and the Fisher Exact Permutation Test.- 4.18.BakerHubert and Ordering Theory.- 4.19.Green and Two Permutation Tests for Location.- 4.20.AgrestiWackerlyBoyett and Approximate Tests.- 4.21.Boyett and Random R by C Tables.- 4.22.Looking Ahead.- 5.19802000.- 5.1.Overview of Chapter 5.- 5.2.Development of Computing.- 5.3.Permutation Methods and Contingency Tables.- 5.4.Yates and 2 by 2 Contingency Tables.- 5.5.MehtaPatel and a Network Algorithm.- 5.6.MRPP and the Pearson type III Distribution.- 5.7.MRPP and Commensuration.- 5.8.Tukey and Re randomization.- 5.9.Matched-pairs Permutation Analysis.- 5.10.Subroutine PERMUT.- 5.11.Moment Approximations and the F Test.- 5.12.MielkeIyer and MRBP.- 5.13.Relationships of MRBP to Other Tests.- 5.14.Kappa and the Measurement of Agreement.- 5.15.Basu and the Fisher Randomization Test.- 5.16.StillWhite and Permutation Analysis of Variance.- 5.17.Walters and the Utility of Resampling Methods.- 5.18.ConoverIman and Rank Transformations.- 5.19.Green and Randomization Tests.- 5.20.GabrielHall and Re randomization Inference.- 5.21.PaganoTritchler and Polynomial-time Algorithms.- 5.22.Welch and a Median Permutation Test.- 5.23.Boik and the FisherPitman Permutation Test.- 5.24.MielkeYao Empirical Coverage Tests.- 5.25.Randomization in Clinical Trials.- 5.26.The Period From 1990 to 2000.- 5.27.Algorithms and Programs.- 5.28.PageBrin and Google.- 5.29.SpinoPagano and Trimmed/Winsorized Means.- 5.30.MayHunter and Advantages of Permutation Tests.- 5.31.MielkeBerry and Tests for Common Locations.- 5.32.KennedyCade and Multiple Regression.- 5.33.Blair et al. and Hotelling's T2 Test.- 5.34.MielkeBerryNeidt and Hotelling's T2 Test.- 5.35.Cade-Richards and Tests for LAD Regression.- 5.36.WalkerLoftisMielke and Spatial Dependence.-  5.37.Frick on Process-based Testing.- 5.38.LudbrookDudley and Biomedical Research.- 5.39...

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A Chronicle of Permutation Statistical Methods
1920-2000, and Beyond
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Springer International Publishing
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