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2016 | Book

Introduction Read chapter Read first chapter

Permutation Statistical Methods

An Integrated Approach

Authors: Kenneth J. Berry, Paul W. Mielke, Jr., Janis E. Johnston

Publisher: Springer International Publishing

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

This research monograph provides a synthesis of a number of statistical tests and measures, which, at first consideration, appear disjoint and unrelated. Numerous comparisons of permutation and classical statistical methods are presented, and the two methods are compared via probability values and, where appropriate, measures of effect size.

Permutation statistical methods, compared to classical statistical methods, do not rely on theoretical distributions, avoid the usual assumptions of normality and homogeneity of variance, and depend only on the data at hand. This text takes a unique approach to explaining statistics by integrating a large variety of statistical methods, and establishing the rigor of a topic that to many may seem to be a nascent field in statistics. This topic is new in that it took modern computing power to make permutation methods available to people working in the mainstream of research.

Table of Contents

Frontmatter
1. Introduction
Abstract
Chapter 1 of Permutation Statistical Methods provides an introduction to the next 10 chapters, presenting and comparing the two models of statistical inference—the population model and the permutation model—and the three main approaches to permutation statistical methods—exact, moment approximation, and resampling approximation. Advantages of permutation statistical methods are elucidated and recursion techniques are described and illustrated.
Kenneth J. Berry, Paul W. Mielke Jr., Janis E. Johnston
2. Completely Randomized Data
Abstract
Chapter 2 introduces a generalized Minkowski distance function that is the basis for a set of multi-response permutation procedures for univariate and multivariate completely randomized data. Multi-response permutation procedures constitute a class of permutation methods for one or more response measurements that are designed to distinguish possible differences among two or more groups. The multi-response permutation procedures provide a synthesizing foundation for a variety of statistical tests and measures developed in successive chapters.
Kenneth J. Berry, Paul W. Mielke Jr., Janis E. Johnston
3. Randomized Designs: Interval Data
Abstract
Chapter 3 utilizes the Multi-Response Permutation Procedures (MRPP) presented in Chap. 2 to develop the relationships between the test statistics of MRPP, δ and \(\mathfrak{R}\), and selected conventional tests and measures designed for the analysis of completely randomized data at the interval level of measurement. The structure of the MRPP test statistic, δ, depends on the choice of v in the generalized Minkowski distance function and the treatment-group weights, C i , i = 1, …, g. Four tests are examined in this chapter: (1) Student’s two-sample t test with interval-level univariate response measurements, (2) Hotelling’s two-sample T 2 test with multivariate interval-level response measurements, (3) one-way fixed-effects analysis of variance (ANOVA) with interval-level univariate response measurements, and (4) one-way multivariate analysis of variance (MANOVA) with interval-level multivariate response measurements.
Kenneth J. Berry, Paul W. Mielke Jr., Janis E. Johnston
4. Regression Analysis of Interval Data
Abstract
Chapter 4 continues Chap. 3, utilizing the multi-response permutation procedures developed in Chap. 2 for analyzing completely randomized data at the interval level of measurement. In Chap. 4, multi-response permutation procedures are used to analyze regression residuals generated by ordinary least squares (OLS) and least absolute deviation (LAD) regression models. Experimental designs presented and analyzed in Chap. 4 include one-way randomized, one-way randomized with a covariate, one-way randomized-block, two-way randomized-block, two-way factorial, Latin square, split-plot, and two-factor nested designs.
Kenneth J. Berry, Paul W. Mielke Jr., Janis E. Johnston
5. Randomized Designs: Ordinal Data, I
Abstract
Chapter 5 utilizes the multi-response permutation procedures (MRPP) developed in Chap. 2 for analyzing completely randomized data at the ordinal level of measurement. The structure of the MRPP test statistic, δ, depends on the choice of v in the generalized Minkowski distance function. A variety of tests are described in this chapter, including the Wilcoxon two-sample rank-sum test, the Kruskal–Wallis multiple-sample rank-sum test, the Ansari–Bradley rank-sum test for dispersion, the Taha sum-of-squared-ranks test, the Mood rank-sum test for dispersion, the Brown–Mood median test, the Mielke power-of-rank function tests, the Whitfield two-sample rank-sum test, and the Cureton rank-biserial test.
Kenneth J. Berry, Paul W. Mielke Jr., Janis E. Johnston
6. Randomized Designs: Ordinal Data, II
Abstract
Chapter 6 utilizes the Multi-Response Permutation Procedures (MRPP) developed in Chap. 2 to establish relationships between the test statistics of MRPP, δ and \(\mathfrak{R}\), and multivariate generalizations of selected conventional tests and measures designed for the analysis of completely randomized data at the ordinal level of measurement. Considered in this chapter are multivariate extensions of the Wilcoxon two-sample rank-sum test, the Kruskal–Wallis multi-sample rank sum test, the Ansari–Bradley rank sum test for dispersion, the Taha sum-of-squared-ranks test, the Mood rank-sum test for dispersion, the Brown–Mood median test, the Mielke A Ns , B Ns , and C Ns power-of-rank function tests, the Whitfield two-sample rank-sum test, and the Cureton rank-biserial test.
Kenneth J. Berry, Paul W. Mielke Jr., Janis E. Johnston
7. Randomized Designs: Nominal Data
Abstract
Chapter 7 utilizes the Multi-Response Permutation Procedures (MRPP) developed in Chap. 2 for analyzing completely randomized data at the nominal (categorical) ordinal level of measurement. The structure of the MRPP test statistic, δ, depends on the choice of v in the generalized Minkowski distance function. A variety of tests are described in this chapter, including Goodman and Kruskal’s t a and t b asymmetric measures of nominal association, Light and Margolin’s categorical analysis of variance, and tests to analyze multiple binary choices.
Kenneth J. Berry, Paul W. Mielke Jr., Janis E. Johnston
8. Randomized Block Data
Abstract
Chapter 8 utilizes a generalized Minkowski distance function as the basis for a set of multivariate block permutation procedures for univariate and multivariate randomized-block data. Multivariate block permutation procedures constitute a class of permutation methods for one or more response measurements in each block that are designed to distinguish possible differences among two or more treatments. The multivariate block permutation procedures provide a synthesizing foundation for a variety of statistical tests and measures developed in successive chapters.
Kenneth J. Berry, Paul W. Mielke Jr., Janis E. Johnston
9. Randomized Block Designs: Interval Data
Abstract
Chapter 9 utilizes the Multivariate Randomized Block Permutation (MRBP) procedures developed in Chap. 8 for analyzing randomized-block data at the interval level of measurement. The structure of the MRBP test statistic, δ, depends on the choice of v in the generalized Minkowski distance function. Four tests are examined in this chapter: (1) Student’s matched-pairs t test with interval-level univariate response measurements, (2) Hotelling’s matched-pairs T 2 test with multivariate interval-level response measurements, (3) one-way randomized-block analysis of variance with interval-level univariate response measurements, and (4) one-way randomized-block analysis of variance with interval-level multivariate response measurements.
Kenneth J. Berry, Paul W. Mielke Jr., Janis E. Johnston
10. Randomized Block Designs: Ordinal Data
Abstract
Chapter 10 utilizes the multivariate randomized-block permutation procedures (MRBP) developed in Chap. 8 for analyzing randomized-block data at the ordinal level of measurement. The structure of the MRBP test statistic, δ, depends on the choice of v in the generalized Minkowski distance function. A variety of tests are described in this chapter, including the Wilcoxon signed-rank test for matched pairs, the sign test, Spearman’s rank-order correlation coefficient and footrule measure, the Kruskal–Wallis analysis of variance for ranks, Kendall’s coefficient of concordance, Cohen’s weighted kappa measure of agreement, Kendall’s τ a and τ b measures of ordinal association, Stuart’s τ c statistic, Goodman and Kruskal’s γ measure of ordinal association, and Somers’ asymmetric measures of ordinal association.
Kenneth J. Berry, Paul W. Mielke Jr., Janis E. Johnston
11. Randomized Block Designs: Nominal Data
Abstract
Chapter 11 utilizes the multivariate randomized-block permutation procedures (MRBP) developed in Chap. 8 for analyzing randomized-block data at the nominal level of measurement. The structure of the MRBP test statistic, δ, depends on the choice of v in the generalized Minkowski distance function. A variety of tests are described in this chapter, including Cohen’s unweighted kappa measure of chance-corrected agreement, McNemar’s test for change, Cochran’s Q test for change, Yule’s Q measure, the odds ratio, Somers’ d xy and d yx asymmetric measures of association, Pearson’s product-moment correlation coefficient, percentage differences, and chi-squared.
Kenneth J. Berry, Paul W. Mielke Jr., Janis E. Johnston
Backmatter
Metadata
Title
Permutation Statistical Methods
Authors
Kenneth J. Berry
Paul W. Mielke, Jr.
Janis E. Johnston
Copyright Year
2016
Electronic ISBN
978-3-319-28770-6
Print ISBN
978-3-319-28768-3
DOI
https://doi.org/10.1007/978-3-319-28770-6

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