Abstract
Motivated by a situation encountered in the Well Elderly 2 study, the paper considers the problem of robust multiple comparisons based on K independent tests associated with 2K independent groups. A simple strategy is to use an extension of Dunnett’s T3 procedure, which is designed to control the probability of one or more Type I errors. However, this method and related techniques fail to take into account the overall pattern of p-values when making decisions about which hypotheses should be rejected. The paper suggests a multiple comparison procedure that does take the overall pattern into account and then describes general situations where this alternative approach makes a practical difference in terms of both power and the probability of one or more Type I errors. For reasons summarized in the paper, the focus is on 20% trimmed means, but in principle the method considered here is relevant to any situation where the Type I error probability of the individual tests can be controlled reasonably well.
Highlights
Considers the situation where K independent tests are performed yielding the p-values p1, ... , pK
When Yuen’s method is applied K times, method YSM consists of controlling familywise error rate (FWE) using a critical value based on the Studentized maximum modulus distribution vjk degrees of freedom, where vjk is the value of vbased on the data associated with groups j and k
All indications are that the step-down method studied here controls FWE fairly well, better than the extension of Yuen’s method, and simultaneously it provides better power, sometimes substantially so
Summary
Considers the situation where K independent tests are performed yielding the p-values p1, ... , pK. Skewed distributions can result in poor control over the Type I error probability and inaccurate confidence intervals (e.g., Wilcox, 2012a, b). These practical concerns are reduced substantially using Yuen's (1974) method (e.g. Wilcox, 2012b). In the event sampling is from normal distributions, power is nearly as high as methods based on means This follows almost immediately from results reported by Rosenberger and Gasko (1983) who studied the efficiency of trimmed means.
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