Two-sample wilcoxon power over the pearson system and comparison with thet-test

The present study has as its object an accurate evaluation of the power of the two-sample equal sample size Wilcoxon test over an extensive practical range of uismnmioriv The method is thai o! a large Monte Carlo study over the Pearson ay item of dmnbuUoiia. β1 = 0.0(0.4)2.0, β2 = 1.4(0.4)7.8 (negative and positive skewness) and equal sample sizes N = 5(5)30. The power is evaluated for two values of the noncentrahty parameter △ (values which produce powers of 0.50 and 0.95 for the corresponding r-test under normality) and these probabilities are evaluated from 40,000 generated values of the test statistic. Since the ingredients of this study are identical to those of a similar earlier study of the t-test, a comparison of the power of the Wilcoxon and the t-test is provided to determine the range of the Pearson system in which the power function of one test is superior to that of the other. The stutly is restricted to equal sample size tests and the results may not apply to more than moderate departures from this condition. Results for the equal sample size case have significant value, however, since this condition is often designed into a study and since the literature suggests that the highest level of robustness is achieved when sample sizes are equal. The results of this study show that, over the range of the Pearson system covered, the power function of the Wilcoxon test is more variable than that of the t-test. Often this variability, particularly in the middle part of the power curve, is favorable to the Wilcoxon test, resulting in higher power for this test. Except for equal sample sizes N = 5, the results, to a large degree, appear to support the recommendation of the nonparametricists who recommend the Wilcoxon test as a general solution for the two-sample location problem. On the other hand, if U- and j-shaped distributions are disregarded, the results show that the power function of the t-test is superior, or “not bad at all”, compared to the Wilcoxon test, over a fairly substantial range of distributions.