Kenneth J. Berry - Permutation Statistical Methods with R

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Dr. Paul W. Mielke, Jr., Professor Emeritus of Statistics at Colorado State University and Fellow of the American Statistical Association, passed away on 20 April 2019.

Permutation Statistical Methods with R presents exact and Monte Carlo permutation statistical methods for generating probability values and measures of effect size for a variety of tests of differences, measures of correlation and association, and measures of goodness of fit. Throughout the book the emphasis is on permutation statistical methods, although the results of permutation analyses are always compared and contrasted with the results of conventional statistical analyses, with which the reader is assumed to be familiar. R Scripts are provided for each conventional test statistic and associated permutation test statistics throughout the book.

Included in tests of differences are one-sample tests, tests of differences for two independent samples, tests of differences for two matched samples, tests of differences for multiple independent samples, and tests of differences for multiple matched samples. Included in measures of correlation and association are simple linear correlation and regression, measures of effect size based on Pearsons chi-squared test statistic, and several other measures of effect size designed for the analysis of contingency tables. The arrangement of the book follows the structure of a typical introductory textbook in statistics: introduction, central tendency and variability, one-sample tests, tests for two independent samples, tests for two matched samples, completely-randomized analysis of variance designs, randomized-blocks analysis of variance designs, simple linear regression and correlation, and the analysis of goodness of fit and contingency.

Chapter is to familiarize the reader with the structure and content of the book and provide a brief introduction to the various permutation tests and measures presented in the following chapters.

Chapter provides an introduction to the R programming language and to RStudio. Although the book is primarily a book on permutation statistical methods and not a book on R per se, the fundamentals of R, as they pertain to permutation methods, are important to present and explain. While the R programming language provides intrinsic (built-in) functions for most conventional statistical tests and measures, the R scripts for permutation statistical tests and measures are not available as intrinsic functions in R and are, as far as the authors know, unique to this book.

Chapter provides an introduction to two models of statistical inference: the population model and the permutation model. Most introductory textbooks in statistics and statistical methods present only the NeymanPearson population model of statistical inference. The NeymanPearson population model of statistical inference is named for Jerzy Neyman (18941981) and Egon Pearson (18951980) and was designed to make inferences about population parameters and provide approximate probability values under the appropriate null hypotheses. The NeymanPearson model is characterized by the assumptions of random sampling, normally-distributed population(s), and homogeneity of variances, where appropriate.

While the NeymanPearson population model will be familiar to most readers and needs little or no introduction, the FisherPitman permutation model of statistical inference is less likely to be familiar to many readers. The FisherPitman permutation model of statistical inference is named for R. A. Fisher (18901962) and E. J. G. Pitman (18971993). In contrast to conventional statistical tests based on the NeymanPearson population model, tests based on the FisherPitman permutation model are distribution-free, entirely data-dependent, appropriate for nonrandom samples, provide exact probability values, and are ideal for small data sets. On the other hand, permutation statistical methods can be computationally intensive, often requiring many millions of calculations. Thus, for the FisherPitman permutation model, exact and Monte Carlo permutation methods are described and compared. Under the NeymanPearson population model, squared Euclidean scaling functions are mandated, while under the FisherPitman permutation model, ordinary Euclidean scaling functions are shown to provide robust alternatives to conventional squared Euclidean scaling functions.

Chapter presents six interactive R scripts for calculating the various measures of central tendency and variability under the NeymanPearson population model and the FisherPitman permutation model.

Chapter presents an introduction to the permutation analysis of one-sample tests. In general, one-sample tests attempt to invalidate a hypothesized value of a population parameter, such as a population mean. Under the NeymanPearson population model, Students conventional one-sample