Experimental comparison of the powers of the two-sample tests of wilcoxon and student under logistic parent distributions

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Abstract
This paper presents the results of an experimental determination by Monte Carlo techniques of the power function of the two-sample rank test of Wilcoxon against shift alternatives for logistic parent distributions. The results of this sampling experiment were based on 5000 trials for each alternative and for each combination of sample sizes. The sample sizes considered arc m=n=3, m=n=6, and m=n=10. The powers of the rank test of Wilcoxon are compared with the experimental powers of the test based on Student's t-test statistic. The results indicate that (i) for m=n=3 and m=n=6 and small sizes of the tests the power of the Wilcoxon test is not much smaller than the power of the t-test, whereas for larger sizes of the tests the difference is smaller and (ii) for m=n=10 and size of the test of about 1%, Wilcoxon's test has somewhat smaller power than Student's test, while for sizes of about 5 and 10% the Wilcoxon test is slightly superior to the t-test.

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