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Introduction to Cochran-Mantel-Haenszel Testing and Nonparametric ANOVA [Kõva köide]

(University of Newcastle, Australia), (University of Newcastle, Australia)
  • Formaat: Hardback, 240 pages, kõrgus x laius x paksus: 244x170x19 mm, kaal: 482 g
  • Sari: Wiley Series in Probability and Statistics
  • Ilmumisaeg: 23-Mar-2023
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1119831989
  • ISBN-13: 9781119831983
Teised raamatud teemal:
Introduction to Cochran-Mantel-Haenszel Testing and Nonparametric ANOVASuurem pilt
  • Formaat: Hardback, 240 pages, kõrgus x laius x paksus: 244x170x19 mm, kaal: 482 g
  • Sari: Wiley Series in Probability and Statistics
  • Ilmumisaeg: 23-Mar-2023
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1119831989
  • ISBN-13: 9781119831983
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781119831983.html
Märksõnad:
"In statistics, the Cochran--Mantel--Haenszel test (CMH) is a test used in the analysis of stratified or matched categorical data. It allows an investigator to test the association between a binary predictor or treatment and a binary outcome such as caseor control status while taking into account the stratification. It is often used in observational studies where random assignment of subjects to different treatments cannot be controlled, but confounding covariates can be measured. The extensions to the Cochran--Mantel--Haenszel (CMH) tests and the nonparametric analysis of variance (NP ANOVA) methodology provide powerful new statistical tests that enable deeper data analysis."--

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.

Preface xiii
1 Introduction
1(8)
1.1 What Are the CMH and NPANOVA Tests?
1(1)
1.2 Outline
2(2)
1.3 Mr
4(1)
1.4 Examples
5(4)
1.4.1 Strawberry Data
5(1)
1.4.2 Homosexual Marriage Data
6(2)
Bibliography
8(1)
2 The Basic CMH Tests
9(20)
2.1 Genesis: Cochran (1954), and Mantel and Haenszel (1959)
9(3)
2.2 The Basic CMH Tests
12(3)
2.2.1 Homosexual Marriage Data
14(1)
2.2.2 Jams Data
14(1)
2.3 The Nominal CMH Tests
15(3)
2.4 The CMH Mean Scores Test
18(1)
2.5 The CMH Correlation Test
19(10)
2.5.1 The CMH C Test Defined
19(2)
2.5.2 An Alternative Presentation of the CMH C Test
21(1)
2.5.3 Examples
22(1)
2.5.3.1 Homosexual Marriage Data
22(1)
2.5.3.2 Whiskey Data
23(1)
2.5.4 Derivation of the CMH C Test Statistic for the RBD with the Same Treatment Scores in Every Stratum
24(1)
2.5.4.1 Jams Data Revisited
25(2)
2.5.5 The CMH C Test Statistic Is Not, in General, Location-Scale Invariant
27(1)
Bibliography
28(1)
3 The Completely Randomised Design
29(22)
3.1 Introduction
29(1)
3.2 The Design and Parametric Model
30(1)
3.3 The Kruskal--Wallis Tests
30(3)
3.3.1 Mid-Rank Lemma
32(1)
3.3.2 Whiskey Data Revisited
33(1)
3.4 Relating the Kruskal-Wallis and ANOVA F Tests
33(2)
3.5 The CMH Tests for the CRD
35(2)
3.5.1 Whiskey Data Revisited
36(1)
3.6 The KW Tests Are CMH MS Tests
37(1)
3.7 Relating the CMH MS and ANOVA F Tests
38(3)
3.7.1 The One-Way ANOVA F Test
38(1)
3.7.2 WMS in Terms of the ANOVA F
38(1)
3.7.3 Whiskey Data Revisited
39(1)
3.7.4 Homosexual Marriage Data Revisited
39(1)
3.7.5 Corn Data
39(2)
3.8 Simulation Study
41(2)
3.9 Wald Test Statistics in the CRD
43(8)
3.9.1 The Wald Test Statistic of General Association for the CMH Design
43(4)
3.9.2 The Wald Test Statistic for the CMH MS Design
47(2)
3.9.3 The Wald Test Statistic for the CMH C Design
49(1)
Bibliography
49(2)
4 The Randomised Block Design
51(22)
4.1 Introduction
51(1)
4.2 The Design and Parametric Model
52(1)
4.3 The Friedman Tests
53(3)
4.3.1 Jams Data
55(1)
4.4 The CMH Test Statistics in the RBD
56(6)
4.4.1 The CMH OPA Test for the RBD
56(1)
4.4.2 The CMH GA Test Statistic for the RBD
56(1)
4.4.3 The CMH MS Test Statistic for the RBD
57(1)
4.4.3.1 Food Products Data
58(2)
4.4.4 The CMH C Test Statistic for the RBD
60(1)
4.4.4.1 Human Resource Data
60(2)
4.5 The Friedman Tests are CMH MS Tests
62(1)
4.6 Relating the CMH MS and ANOVA F Tests
63(2)
4.6.1 Jams Data Revisited
65(1)
4.7 Simulation Study
65(3)
4.8 Wald Test Statistics in the RBD
68(5)
Bibliography
72(1)
5 The Balanced Incomplete Block Design
73(24)
5.1 Introduction
73(1)
5.2 The Durbin Tests
73(1)
5.3 The Relationship Between the Adjusted Durbin Statistic and the ANOVA F Statistic
74(5)
5.3.1 Ice Cream Flavouring Data
76(2)
5.3.2 Breakfast Cereal Data
78(1)
5.4 Simulation Study
79(3)
5.5 Orthogonal Contrasts for Balanced Designs with Ordered Treatments
82(11)
5.5.1 Orthogonal Contrasts
82(1)
5.5.2 Orthogonal Contrasts for Nonparametric Testing in Balanced Designs
83(2)
5.5.2.1 The RBD Example
85(1)
5.5.2.2 The BIBD Example
86(1)
5.5.3 F Orthogonal Contrasts
87(1)
5.5.3.1 The RBD Example
88(1)
5.5.3.2 Lemonade Taste Example
88(1)
5.5.3.3 The BIBD Example
89(1)
5.5.3.4 Ice Cream Flavouring Data
89(1)
5.5.4 Simulation Study
90(3)
5.6 A CMH MS Analogue Test Statistic for the BIBD
93(4)
5.6.1 Ice Cream Flavouring Data
95(1)
Bibliography
95(2)
6 Unconditional Analogues of CMH Tests
97(28)
6.1 Introduction
97(2)
6.1.1 Jams Data Revisited
98(1)
6.2 Unconditional Univariate Moment Tests
99(3)
6.2.1 RBD Example
101(1)
6.3 Generalised Correlations
102(8)
6.3.1 Bivariate Generalised Correlations
102(3)
6.3.1 Age and Intelligence Data
105(2)
6.3.3 Trivariate Generalised Correlations
107(1)
6.3.4 Lizard Data
107(3)
6.4 Unconditional Bivariate Moment Tests
110(3)
6.4.1 Homosexual Marriage Data
111(2)
6.5 Unconditional General Association Tests
113(7)
6.5.1 Cross-Over Clinical Data
118(1)
6.5.2 Saltiness Data
119(1)
6.6 Stuart's Test
120(5)
Bibliography
123(2)
7 Higher Moment Extensions to the Ordinal CMH Tests
125(12)
7.1 Introduction
125(1)
7.2 Extensions to the CMH Mean Scores Test
125(3)
7.3 Extensions to the CMH Correlation Test
128(3)
7.4 Examples
131(6)
7.4.1 Jams Data
131(3)
7.4.2 Homosexual Marriage Data
134(2)
Bibliography
136(1)
8 Unordered Nonparametric ANOVA
137(18)
8.1 Introduction
137(3)
8.1.1 Strawberry Data
139(1)
8.2 Unordered NP ANOVA for the CMH Design
140(1)
8.3 Singly Ordered Three-Way Tables
141(3)
8.4 The Kruskal--Wallis and Friedman Tests Are NP ANOVA Tests
144(3)
8.4.1 The Kruskal--Wallis, ANOVA F, and NP ANOVA F Tests on the Ranks Are All Equivalent
144(1)
8.4.2 The Friedman, ANOVA F, and NP ANOVA F Tests Are All Equivalent
145(2)
8.5 Are the CMH MS and Extensions NP ANOVA Tests?
147(2)
8.5.1 Jams Data
147(2)
8.6 Extension to Other Designs
149(1)
8.6.1 Aside. The Friedman Test Revisited
150(1)
8.7 Latin Squares
150(3)
8.7.1 Traffic Data
151(2)
8.8 Balanced Incomplete Blocks
153(2)
8.8.1 Ice Cream Flavouring Data Revisited
153(1)
Bibliography
154(1)
9 The Latin Square Design
155(26)
9.1 Introduction
155(1)
9.2 The Latin Square Design and Parametric Model
156(1)
9.3 The RL Test
157(1)
9.4 Alignment
158(4)
9.5 Simulation Study
162(6)
9.6 Examples
168(6)
9.6.1 Dynamite Data
168(2)
9.6.2 Peanuts Data
170(2)
9.6.3 Traffic Data
172(2)
9.7 Orthogonal Trend Contrasts for Ordered Treatments
174(4)
9.7.1 Dynamite Data Revisited
174(2)
9.7.2 Peanut Data Revisited
176(1)
9.7.3 Traffic Data Revisited
176(2)
9.8 Technical Derivation of the RL Test
178(3)
Bibliography
180(1)
10 Ordered Non-parametric ANOVA
181(24)
10.1 Introduction
181(3)
10.1.1 Strawberry Data Revisited
181(3)
10.2 Ordered NP ANOVA for the CMH Design
184(1)
10.3 Doubly Ordered Three-Way Tables
185(2)
10.3.1 Whiskey Data Revisited
187(1)
10.3.2 Jams Data Revisited
187(1)
10.4 Extension to Other Designs
187(2)
10.5 Latin Square Rank Tests
189(3)
10.5.1 Doubly Ordered Four-Way Tables
189(3)
10.6 Modelling the Moments of the Response Variable
192(4)
10.7 Lemonade Sweetness Data
196(6)
10.8 Breakfast Cereal Data Revisited
202(3)
Bibliography
204(1)
11 Conclusion
205(12)
11.1 CMH or NP ANOVA?
205(1)
11.2 Homosexual Marriage Data Revisited for the Last Time!
206(3)
11.3 Job Satisfaction Data
209(5)
11.4 The End
214(3)
Bibliography
215(2)
Appendix A Appendix
217(3)
A.1 Kronecker Products and Direct Sums
217(2)
A.2 The Moore--Penrose Generalised Inverse
219(1)
Subject Index 220(2)
Reference Index 222(2)
Data Index 224
John Charles William Rayner 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.

Glen Livingston, Jr., is a Lecturer, School of Mathematical and Physical Sciences, University of Newcastle, Australia.