Abstract
We consider multiple tests for the differences among propotions in k binomial populations. The simultaneous confidence intervals for all the pairwise differences among the propotions are expressed in Hochberg and Tamhane (1987). We may propose the Tukey-Kramer type multiple tests similar to the simultaneous confidence intervals. However the degree of the conservativeness for the multiple tests depends on unknown parameters. Therefore multiple tests based on arcsin transformation are proposed. It is shown that the degree of the conservativeness for the proposed tests is controled by the sized of the samples. For the multiple comparisons with a control, the multiple test procedures based on the Bonferroni inequality are stated in Shiraishi (2009), and Tanaka and Tarumi (1997). Using the arcsin transformation, the Dunnett-type multiple tests superior to the former tests are discussed. Furthermore the closed testing procedures more powerful than the Tukey-Welsch tests and the REGW tests are proposed. Lastly a sequentially rejective procedure is discussed.
