Using simulation studies, Day and Quinn (1989) COMPARISONS OF TREATMENTS AFTER AN ANALYSIS OF VARIANCE IN ECOLOGY showed that the Tukey method is conservative with respect to Type I error rate; in Fig 1 you can see that the actual Type I error rate is about 0.02 when the nominal rate is 0.05 for their simulation scenario. Consequently, Type II error rate also is excessively increased (i.e., you lose more power). There's no perfect solution 🙂
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