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Editor: Austin and Goldwasser  missed a key opportunity to point out that in fact it is perfectly valid to use the data to select the cutoff for dichotomization in a 2xk contingency table as long as the proper penalty is paid for doing do. In general, this penalty tends not to be so great, and the approach saves one from having to pretend to know prospectively where the treatment effect will manifest itself maximally. In fact, an adaptive approach can be used whenever any one of several analyses may prove to be the most impressive. One simply computes each p-value, selects the lowest among these, and then uses it not as a p-value per se but rather as a test statistic for use with a design-based permutation test . The question is how low is this lowest p-value relative not to a uniform distribution on the unit interval but rather relative to the permutation distribution of similarly computed minimum p-values. This latter reference distribution will, of course, be stochastically smaller than a uniform distribution on the unit interval, so the raw minimum p-value will be adjusted upwards by filtering it through this validation transformation. When all analyses considered are binary analyses resulting from dichotomizing a categorical endpoint all possible ways (the Lancaster decomposition), the adaptive test described reduces to the Smirnov test .
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