An Introduction to Cochran-Mantel-Haenszel Testing and Nonparametric ANOVA

J. C. W. Rayner , G. C. Livingston, Jr. 지음

Wiley 2023년 02월 14일 출간

작품소개

책소개

An Introduction to Cochran-Mantel-Haenszel Testing and Nonparametric ANOVA Complete reference for applied statisticians and data analysts that uniquely covers the new statistical methodologies that enable deeper data analysis An Introduction to Cochran-Mantel-Haenszel Testing and Nonparametric ANOVA provides readers with powerful new statistical methodologies that enable deeper data analysis. The book offers applied statisticians an introduction to the latest topics in nonparametrics. The worked examples with supporting R code provide analysts the tools they need to apply these methods to their own problems. Co-authored by an internationally recognised expert in the field and an early career researcher with broad skills including data analysis and R programming, the book discusses key topics such as: NP ANOVA methodology Cochran-Mantel-Haenszel (CMH) methodology and design Latin squares and balanced incomplete block designs Parametric ANOVA F tests for continuous data Nonparametric rank tests (the Kruskal-Wallis and Friedman tests) CMH MS tests for the nonparametric analysis of categorical response data Applied statisticians and data analysts, as well as students and professors in data analysis, can use this book to gain a complete understanding of the modern statistical methodologies that are allowing for deeper data analysis.

목차

Preface xiii 1 Introduction 1 1.1 What are the CMH and NP ANOVA tests? 1 1.2 Outline 3 1.3 5 1.4 Examples 6 2 The Basic CMH Tests 13 2.1 Genesis: Cochran (1954), and Mantel and Haenszel (1959) 13 2.2 The basic CMH tests 18 2.3 The Nominal CMH tests 22 2.4 The CMH mean scores test 26 2.5 The CMH correlation test 28 3 The Completely Randomised Design 41 3.1 Introduction 41 3.2 The design and parametric model 42 3.3 The Kruskal-Wallis tests 43 3.4 Relating the Kruskal-Wallis and ANOVA F tests 47 3.5 The CMH tests for the CRD 49 3.6 The KW tests are CMH MS tests 52 3.7 Relating the CMH MS and ANOVA F tests 54 3.8 Simulation study 58 3.9 Wald test statistics in the CRD 61 4 The Randomised Block Design 71 4.1 Introduction 71 4.2 The design and parametric model 72 4.3 The Friedman tests 74 4.4 The CMH test statistics in the RBD 77 4.5 The Friedman tests are CMH MS tests 86 4.6 Relating the CMH MS and ANOVA F tests 88 4.7 Simulation study 91 4.8 Wald test statistics in the RBD 94 5 The Balanced Incomplete Block Design 101 5.1 Introduction 101 5.2 The Durbin tests 101 5.3 The relationship between the adjusted Durbin statistic and the ANOVA F statistic 103 5.4 Simulation study 110 5.5 Orthogonal contrasts for balanced designs with ordered treatments 113 5.6 A CMH MS analogue test statistic for the BIBD 124 6 Unconditional Analogues of CMH Tests 129 6.1 Introduction 129 6.2 Unconditional univariate moment tests 132 6.3 Generalised correlations 137 6.4 Unconditional bivariate moment tests 147 6.5 Unconditional general association tests 152 6.6 Stuart’s Test 163 7 Higher Moment Extensions To The Ordinal CMH Tests 167

작가정보

저자(글) J. C. W. Rayner

저자(글) G. C. Livingston, Jr.

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