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

Cover
Title Page
Copyright
Contents
Preface
Chapter 1 Introduction
1.1 What Are the CMH and NP ANOVA Tests?
1.2 Outline
1.3 R
1.4 Examples
1.4.1 Strawberry Data
1.4.2 Homosexual Marriage Data
Bibliography
Chapter 2 The Basic CMH Tests
2.1 Genesis: Cochran (1954), and Mantel and Haenszel (1959)
2.2 The Basic CMH Tests
2.2.1 Homosexual Marriage Data
2.2.2 Jams Data
2.3 The Nominal CMH Tests
2.4 The CMH Mean Scores Test
2.5 The CMH Correlation Test
2.5.1 The CMH C Test Defined
2.5.2 An Alternative Presentation of the CMH C Test
2.5.3 Examples
2.5.3.1 Homosexual Marriage Data
2.5.3.2 Whiskey Data
2.5.4 Derivation of the CMH C Test Statistic for the RBD with the Same Treatment Scores in Every Stratum
2.5.4.1 Jams Data Revisited
2.5.5 The CMH C Test Statistic Is Not, in General, Location‐Scale Invariant
Bibliography
Chapter 3 The Completely Randomised Design
3.1 Introduction
3.2 The Design and Parametric Model
3.3 The Kruskal–Wallis Tests
3.3.1 Mid‐Rank Lemma
3.3.2 Whiskey Data Revisited
3.4 Relating the Kruskal–Wallis and ANOVA F Tests
3.5 The CMH Tests for the CRD
3.5.1 Whiskey Data Revisited
3.6 The KW Tests Are CMH MS Tests
3.7 Relating the CMH MS and ANOVA F Tests
3.7.1 The One‐Way ANOVA F Test
3.7.2 WMS in Terms of the ANOVA F
3.7.3 Whiskey Data Revisited
3.7.4 Homosexual Marriage Data Revisited
3.7.5 Corn Data
3.8 Simulation Study
3.9 Wald Test Statistics in the CRD
3.9.1 The Wald Test Statistic of General Association for the CMH Design
3.9.2 The Wald Test Statistic for the CMH MS Design
3.9.3 The Wald Test Statistic for the CMH C Design
Bibliography
Chapter 4 The Randomised Block Design
4.1 Introduction
4.2 The Design and Parametric Model
4.3 The Friedman Tests
4.3.1 Jams Data
4.4 The CMH Test Statistics in the RBD
4.4.1 The CMH OPA Test for the RBD
4.4.2 The CMH GA Test Statistic for the RBD
4.4.3 The CMH MS Test Statistic for the RBD
4.4.3.1 Food Products Data
4.4.4 The CMH C Test Statistic for the RBD
4.4.4.1 Human Resource Data
4.5 The Friedman Tests are CMH MS Tests
4.6 Relating the CMH MS and ANOVA F Tests
4.6.1 Jams Data Revisited
4.7 Simulation Study
4.8 Wald Test Statistics in the RBD
Bibliography
Chapter 5 The Balanced Incomplete Block Design
5.1 Introduction
5.2 The Durbin Tests
5.3 The Relationship Between the Adjusted Durbin Statistic and the ANOVA F Statistic
5.3.1 Ice Cream Flavouring Data
5.3.2 Breakfast Cereal Data
5.4 Simulation Study
5.5 Orthogonal Contrasts for Balanced Designs with Ordered Treatments
5.5.1 Orthogonal Contrasts
5.5.2 Orthogonal Contrasts for Nonparametric Testing in Balanced Designs
5.5.2.1 The RBD Example
5.5.2.2 The BIBD Example
5.5.3 F Orthogonal Contrasts
5.5.3.1 The RBD Example
5.5.3.2 Lemonade Taste Example
5.5.3.3 The BIBD Example
5.5.3.4 Ice Cream Flavouring Data
5.5.4 Simulation Study
5.6 A CMH MS Analogue Test Statistic for the BIBD
5.6.1 Ice Cream Flavouring Data
Bibliography
Chapter 6 Unconditional Analogues of CMH Tests
6.1 Introduction
6.1.1 Jams Data Revisited
6.2 Unconditional Univariate Moment Tests
6.2.1 RBD Example
6.3 Generalised Correlations
6.3.1 Bivariate Generalised Correlations
6.3.2 Age and Intelligence Data
6.3.3 Trivariate Generalised Correlations
6.3.4 Lizard Data
6.4 Unconditional Bivariate Moment Tests
6.4.1 Homosexual Marriage Data
6.5 Unconditional General Association Tests
6.5.1 Cross‐Over Clinical Data
6.5.2 Saltiness Data
6.6 Stuart's Test
Bibliography
Chapter 7 Higher Moment Extensions to the Ordinal CMH Tests
7.1 Introduction
7.2 Extensions to the CMH Mean Scores Test
7.3 Extensions to the CMH Correlation Test
7.4 Examples
7.4.1 Jams Data
7.4.2 Homosexual Marriage Data
Bibliography
Chapter 8 Unordered Nonparametric ANOVA
8.1 Introduction
8.1.1 Strawberry Data
8.2 Unordered NP ANOVA for the CMH Design
8.3 Singly Ordered Three‐Way Tables
8.4 The Kruskal–Wallis and Friedman Tests Are NP ANOVA Tests
8.4.1 The Kruskal–Wallis, ANOVA F, and NP ANOVA F Tests on the Ranks Are All Equivalent
8.4.2 The Friedman, ANOVA F, and NP ANOVA F Tests Are All Equivalent
8.5 Are the CMH MS and Extensions NP ANOVA Tests?
8.5.1 Jams Data
8.6 Extension to Other Designs
8.6.1 Aside. The Friedman Test Revisited
8.7 Latin Squares
8.7.1 Traffic Data
8.8 Balanced Incomplete Blocks
8.8.1 Ice Cream Flavouring Data Revisited
Bibliography
Chapter 9 The Latin Square Design
9.1 Introduction
9.2 The Latin Square Design and Parametric Model
9.3 The RL Test
9.4 Alignment
9.5 Simulation Study
9.6 Examples
9.6.1 Dynamite Data
9.6.2 Peanuts Data
9.6.3 Traffic Data
9.7 Orthogonal Trend Contrasts for Ordered Treatments
9.7.1 Dynamite Data Revisited
9.7.2 Peanut Data Revisited
9.7.3 Traffic Data Revisited
9.8 Technical Derivation of the RL Test
Bibliography
Chapter 10 Ordered Non‐parametric ANOVA
10.1 Introduction
10.1.1 Strawberry Data Revisited
10.2 Ordered NP ANOVA for the CMH Design
10.3 Doubly Ordered Three‐Way Tables
10.3.1 Whiskey Data Revisited
10.3.2 Jams Data Revisited
10.4 Extension to Other Designs
10.5 Latin Square Rank Tests
10.5.1 Doubly Ordered Four‐Way Tables
10.6 Modelling the Moments of the Response Variable
10.7 Lemonade Sweetness Data
10.8 Breakfast Cereal Data Revisited
Bibliography
Chapter 11 Conclusion
11.1 CMH or NP ANOVA?
11.2 Homosexual Marriage Data Revisited for the Last Time!
11.3 Job Satisfaction Data
11.4 The End
Bibliography
Appendix A Appendix
A.1 Kronecker Products and Direct Sums
A.2 The Moore–Penrose Generalised Inverse
Subject Index
References Index
Data Index
EULA