2012 Volume 39 Issue 2 Pages 167-182
First, we consider multiple comparisons for the differences among parameters in k Poisson populations. We may give the Tukey-Kramer type multiple test procedure based on estimators of k means. However, the degree of conservativeness for the multiple tests depends on unknown rate parameters. Therefore, multiple tests based on estimators of k standard deviations are proposed. It is found that the degree of conservativeness for the proposed tests is controlled by the sample sizes. Furthermore, the closed testing procedure, more powerful than the REGW (Ryan⁄Einot-Gabriel⁄Welsch) tests, is proposed. Simultaneous confidence intervals for the differences of the square roots of the rates are discussed.
Next, for the multiple comparisons with a control, we propose the multiple test procedure based on the estimators of k standard deviations. It is shown that the proposed multiple test is superior to the tests based on the Bonferroni inequality asymptotically. A sequentially rejective procedure is derived under unequal sample sizes.