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.