A unified sequential test procedure for simultaneous testing the equality of several binomial proportions to a specified standard

In this article, we propose a unified sequentially rejective test procedure for testing simultaneously the equality of several independent binomial proportions to a specified standard. The proposed test procedure is general enough to include some well-known multiple testing procedures such as the Ordinary Bonferroni procedure, Hochberg procedure and Rom procedure. It involves multiple tests of significance based on the simple binomial tests (exact or approximate) which can be easily found in many elementary standard statistics textbooks. Unlike the traditional Chi-square test of the overall hypothesis, the procedure can identify the subset of the binomial proportions, which are different from the prespecified standard with the control of the familywise type I error rate. Moreover, the power computation of the procedure is provided and the procedure is illustrated by two real examples from an ecological study and a carcinogenicity study.