Tarone (1990, Biometrics 46, 515-522) proposed a multiple test procedure for discrete test statistics improving the usual Bonferroni procedure. However, Tarone's procedure is not monotone depending on the predetermined multiple level a. Roth (1998, Journal of Statistical Planning and Inference, in press) developed a monotone version of Tarone's procedure. We present a similar procedure that is both monotone and an improvement of Tarone's proposal. Based on this extension, we derive a step-down procedure that is a corresponding improvement of Holm's (1979, Scandinavian Journal of Statistics 6, 65-70) sequentially rejective procedure. It is shown how adjusted p-values can be computed for the monotone procedures. Finally, the described ideas are applied to the concept of Riiger tests.
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Hommel et al. (1998) studied this question.
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