Comparison of Some Two-Sample Location Tests for Non-Normal Alternatives

Abstract

Summary Small to moderate sample size performance of the two‐sample χ2, Kolmogorov–Smirnov, Wilcoxon and F‐tests of location is investigated in a class of non‐normal distributions through Monte Carlo sampling. The class of distributions is that of mixtures of two normal distributions with different means and/or variances. The cases of mixtures considered represent part of the regions for types I, II, IV, VI and VII of the Pearson system of continuous distributions. The mixture distributions from which the samples are drawn differ only in means, and possess varying degrees of skewness and kurtosis. Based on the Monte Carlo results, the Wilcoxon and Kolmogorov–Smirnov tests generally have higher power than the F‐test, except for near normal underlying distributions where the F‐test is optimal. The power of the χ2 test is less than optimal except when the sample size is large.

Nonparametric Sequential Comparison of Two Treatments with Random Allocation

“…The common variance is 2 = 1 − + c 2 + 1 − a 2 . Formulas for skewness and kurtosis can be found in Afifi and Kim (1972). We have considered populations generated from all combinations of c = 1 2 3; a = 0 0 51 2 56; = 0 1 0 3; and = 0 0 8.…”

“…We employ a class of location and scale-contaminated normal distributions used by Afifi and Kim (1972). With probability we sample from the mixture population…”