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This book focuses on multiple comparisons of proportions in multi-sample models with Bernoulli responses. First, the author explains the one-sample and two-sample methods that form the basis of multiple comparisons. Then, regularity conditions are stated in detail. Simultaneous inference for all proportions based on exact confidence limits and based on asymptotic theory is discussed. Closed testing procedures based on some one-sample statistics are introduced. For all-pairwise multiple comparisons of proportions, the author uses arcsine square root transformation of sample means. Closed testing procedures based on maximum absolute values of some two-sample test statistics and based on chi-square test statistics are introduced. It is shown that the multi-step procedures are more powerful than single-step procedures and the Ryan-Einot-Gabriel-Welsch (REGW)-type tests. Furthermore, the author discusses multiple comparisons with a control. Under simple ordered restrictions of proportions, the author also discusses closed testing procedures based on maximum values of two-sample test statistics and based on Bartholomew's statistics. Last, serial gatekeeping procedures based on the above-mentioned closed testing procedures are proposed although Bonferroni inequalities are used in serial gatekeeping procedures of many.
List of contents
Theoretical Basics in One-Sample and Two-Sample Models.- Simultaneous Inference for All Proportions.- All-Pairwise Comparison Tests.- Multiple Comparison Tests with a Control.- Simultaneous Confidence Intervals.- All-Pairwise Comparisons under Simple Order Restrictions.- Comparisons with a Control and Successive Comparisons under Simple Order Restrictions.- Comparisons with a Control and Successive Comparisons under Simple Order Restrictions.- Hybrid Serial Gatekeeping Procedures for Multiple Comparisons With a Control.
About the author
Taka-aki Shiraishi, Nanzan University
