Combining the t test and Wilcoxon's rank-sum test

In the two-sample location-shift problem, Student's t test or Wilcoxon's rank-sum test are commonly applied. The latter test can be more powerful for non-normal data. Here, we propose to combine the two tests within a maximum test. We show that the constructed maximum test controls the type I error rate and has good power characteristics for a variety of distributions; its power is close to that of the more powerful of the two tests. Thus, irrespective of the distribution, the maximum test stabilizes the power. To carry out the maximum test is a more powerful strategy than selecting one of the single tests. The proposed test is applied to data of a clinical trial.