The authors performed a Monte Carlo simulation to empirically investigate the robustness and power of 4 methods in testing mean differences for 2 independent groups under conditions in which 2 populations may not demonstrate the same pattern of nonnormality. The approaches considered were the t test, Wilcoxon rank-sum test, Welch-James test with…

The authors generated exact probability distributions for sample sizes up to 35 in each of three groups ("n" less than or equal to 105) and up to 10 in each of four groups ("n" less than or equal to 40). They compared the exact distributions to the chi-square, gamma, and beta approximations. The beta approximation was best in…

The power functions of Student t tests performed on initial scores, ordinary ranks, 3 kinds of modular ranks, and dichotomies were investigated for 1 normal and 3 nonnormal distributions using 2 samples of 26 simulated scores each. Advantages of extending the rank transformation concept are discussed. (SLD)

It is argued that outlier-prone distributions reduce the power of nonparametric tests, but power can be restored through procedures usually associated with parametric tests. Computer simulation is used to show how an outlier detection and downweighting procedure augments the power of the t-test and the Wilcoxon-Mann-Whitney test. (SLD)

Assessed the relative merits of the Student "t" test and the Wilcoxon rank sum test under four population distributions and six sample-size pairings through Monte Carlo methods. The Wilcoxon rank sum test demonstrated an advantage in statistical power for nonnormal distributions (but not normal distributions), with fewer Type III errors…

Nonparametric and robust statistics (those using trimmed means and Winsorized variances) were compared for their ability to detect treatment effects in the two-sample case. The use of two specialized tests, designed to be sensitive to treatment effects when data distributions are skewed to the right, is not supported by the analyses. (SLD)

Type I error rate and power for the t test, Wilcoxon-Mann-Whitney test, van der Waerden Normal Scores, and Welch-Aspin-Satterthwaite (W) test are compared for two simulated independent random samples from nonnormal distributions. Conditions under which the t test and W test are best to use are discussed. (SLD)

A program obtained random samples from known populations, some of which violated the homogeneity assumption. Student t tests and Mann-Whitney U Tests were performed on the sample value. Where the t test led to incorrect decisions, the use of Mann-Whitney U test in its place led to poorer results. (JAZ)