Details

<p>Preface xiii</p> <p><b>1 Introduction 1</b></p> <p>1.1 What are the CMH and NP ANOVA tests? 1</p> <p>1.2 Outline 3</p> <p>1.3 5</p> <p>1.4 Examples 6</p> <p><b>2 The Basic CMH Tests 13</b></p> <p>2.1 Genesis: Cochran (1954), and Mantel and Haenszel (1959) 13</p> <p>2.2 The basic CMH tests 18</p> <p>2.3 The Nominal CMH tests 22</p> <p>2.4 The CMH mean scores test 26</p> <p>2.5 The CMH correlation test 28</p> <p><b>3 The Completely Randomised Design 41</b></p> <p>3.1 Introduction 41</p> <p>3.2 The design and parametric model 42</p> <p>3.3 The Kruskal-Wallis tests 43</p> <p>3.4 Relating the Kruskal-Wallis and ANOVA F tests 47</p> <p>3.5 The CMH tests for the CRD 49</p> <p>3.6 The KW tests are CMH MS tests 52</p> <p>3.7 Relating the CMH MS and ANOVA F tests 54</p> <p>3.8 Simulation study 58</p> <p>3.9 Wald test statistics in the CRD 61</p> <p><b>4 The Randomised Block Design 71</b></p> <p>4.1 Introduction 71</p> <p>4.2 The design and parametric model 72</p> <p>4.3 The Friedman tests 74</p> <p>4.4 The CMH test statistics in the RBD 77</p> <p>4.5 The Friedman tests are CMH MS tests 86</p> <p>4.6 Relating the CMH MS and ANOVA F tests 88</p> <p>4.7 Simulation study 91</p> <p>4.8 Wald test statistics in the RBD 94</p> <p><b>5 The Balanced Incomplete Block Design 101</b></p> <p>5.1 Introduction 101</p> <p>5.2 The Durbin tests 101</p> <p>5.3 The relationship between the adjusted Durbin statistic and the ANOVA F statistic 103</p> <p>5.4 Simulation study 110</p> <p>5.5 Orthogonal contrasts for balanced designs with ordered treatments 113</p> <p>5.6 A CMH MS analogue test statistic for the BIBD 124</p> <p><b>6 Unconditional Analogues of CMH Tests 129</b></p> <p>6.1 Introduction 129</p> <p>6.2 Unconditional univariate moment tests 132</p> <p>6.3 Generalised correlations 137</p> <p>6.4 Unconditional bivariate moment tests 147</p> <p>6.5 Unconditional general association tests 152</p> <p>6.6 Stuart’s Test 163</p> <p><b>7 Higher Moment Extensions To The Ordinal CMH Tests 167</b></p> <p>7.1 Introduction 167</p> <p>7.2 Extensions to the CMH mean scores test 168</p> <p>7.3 Extensions to the CMH correlation test 172</p> <p>7.4 Examples 176</p> <p><b>8 Unordered Nonparametric ANOVA 183</b></p> <p>8.1 Introduction 183</p> <p>8.2 Unordered NP ANOVA for the CMH design 187</p> <p>8.3 Singly ordered three-way tables 189</p> <p>8.4 The Kruskal-Wallis and Friedman tests are NP ANOVA tests 193</p> <p>8.5 Are the CMH MS and extensions NP ANOVA tests? 197</p> <p>8.6 Extension to other designs 199</p> <p>8.7 Latin squares 202</p> <p>8.8 Balanced incomplete blocks 204</p> <p><b>9 The Latin Square Design 207</b></p> <p>9.1 Introduction 207</p> <p>9.2 The Latin square design and parametric model 208</p> <p>9.3 The RL test 210</p> <p>9.4 Alignment 212</p> <p>9.5 Simulation study 216</p> <p>9.6 Examples 225</p> <p>9.7 Orthogonal trend contrasts for ordered treatments 232</p> <p>9.8 Technical derivation of the RL test 238</p> <p><b>10 Ordered Nonparametric ANOVA 243</b></p> <p>10.1 Introduction 243</p> <p>10.2 Ordered NP ANOVA for the CMH design 247</p> <p>10.3 Doubly ordered three-way tables 249</p> <p>10.4 Extension to other designs 252</p> <p>10.5 Latin square rank tests 255</p> <p>10.6 Modelling the moments of the response variable 257</p> <p>10.7 Lemonade sweetness data 262</p> <p>10.8 Breakfast cereal data revisited 271</p> <p><b>11 Conclusion 275</b></p> <p>11.1 CMH or NP ANOVA? 275</p> <p>11.2 Homosexual marriage data revisited for the last time! 277</p> <p>11.3 Job satisfaction data 280</p> <p>11.4 The end 286</p> <p><b>A Appendix 289</b></p> <p>A.1 Kronecker Products and Direct Sums 289</p> <p>A.2 The Moore-Penrose Generalised Inverse 292</p>

<p><b>John Charles William Rayner</b> is an Honorary Professorial Fellow, National Institute for Applied Statistics Research Australia, University of Wollongong, and Conjoint Professor of Statistics, School of Mathematical and Physical Sciences, University of Newcastle, Australia.</p> <p><b>Glen Livingston, Jr.,</b> is a Lecturer, School of Mathematical and Physical Sciences, University of Newcastle, Australia.

<p><b>Complete reference for applied statisticians and data analysts that uniquely covers the new statistical methodologies that enable deeper data analysis</b></p> <p><i>An Introduction to Cochran-Mantel-Haenszel Testing and Nonparametric ANOVA</i> 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. <p>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: <ul><li>NP ANOVA methodology</li> <li>Cochran-Mantel-Haenszel (CMH) methodology and design</li> <li>Latin squares and balanced incomplete block designs</li> <li>Parametric ANOVA F tests for continuous data</li> <li>Nonparametric rank tests (the Kruskal-Wallis and Friedman tests)</li> <li>CMH MS tests for the nonparametric analysis of categorical response data</li></ul> <p>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.

GB