The Effect of Non‐normality on the Power of Randomization Tests: A Simulation Study Using Normal Mixtures

In this paper we evaluate the impact of non‐normally on the power of randomization tests for two independent groups with the fifteen densities used in Marron and Wand [19] simulation study, which can all be written as normal mixtures and are believed to model many real data situations. We evaluate the power of the randomization test, and also the power of the Student‐t test, as a comparison standard, with data simulated from the fifteen Marron‐Wand distributions, for 81 values of effect size (from –4.0 to 4.0, by steps of 0.1) and balanced samples of 8, 16 and 32 elements. For each situation, using modules written in R [27], we have generated 20,000 samples and, for each of these, the power of the randomization tests was estimated using 1,000 data permutations. We set the value of Type I error probability at 0.05. In general, the results show that non‐normality has a moderate influence on the power of the randomizations tests and that this influence reduces with increasing sample size. When we compare the...