Comparison of the Power of Bootstrap Two-Sample Test and Wilcoxon Rank Sum Test for Positively Skewed Population

This research examines the power of bootstrap two-sample test, and compares it with the powers of two-sample t-test and Wilcoxon rank sum test, through simulation. For simulation work, a positively skewed and heavy tailed distribution was selected as a population distribution, the chi-square distributions with three degrees of freedom, χ²₃. For two independent samples, the fist sample was selected from χ²₃. The second sample was selected independently from the same χ²₃ as the first sample, and calculated d+ax for each sampled value x, a randomly selected value from χ²₃. The d in d+ax has from 0 to 5 by 0.5 interval, and the a has from 1.0 to 1.5 by 0.1 interval. The powers of three methods were evaluated for the sample sizes 10,20,30,40,50. The null hypothesis was the two population medians being equal for Bootstrap two-sample test and Wilcoxon rank sum test, and the two population means being equal for the two-sample t-test. The powers were obtained using r program language; wilcox.test() in r base package for Wilcoxon rank sum test, t.test() in r base package for the two-sample t-test, boot.two.bca() in r wBoot pacakge for the bootstrap two-sample test. Simulation results show that the power of Wilcoxon rank sum test is the best for all 330 (n,a,d) combinations and the power of two-sample t-test comes next, and the power of bootstrap two-sample comes last. As the results, it can be recommended to use the classic inference methods if there are widely accepted and used methods, in terms of time, costs, sometimes power.