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…

Increasing the correlation between the independent variable and the mediator ("a" coefficient) increases the effect size ("ab") for mediation analysis; however, increasing a by definition increases collinearity in mediation models. As a result, the standard error of product tests increase. The variance inflation caused by…

Randomization tests are often recommended when parametric assumptions may be violated because they require no distributional or random sampling assumptions in order to be valid. In addition to being exact, a randomization test may also be more powerful than its parametric counterpart. This was demonstrated in a simulation study which examined the…

Tests of the equality of variances are sometimes used on their own to compare variability across groups of experimental or non-experimental conditions but they are most often used alongside other methods to support assumptions made about variances. A new nonparametric test of equality of variances is described and compared to current "gold…

The distance between nonparametric and parametric item characteristic curves has been proposed as an index of goodness of fit in item response theory in the form of a root integrated squared error index. This article proposes to use the posterior distribution of the latent trait as the nonparametric model and compares the performance of an index…

A resampling-based method of inference--permutation tests--is often used when distributional assumptions are questionable or unmet. Not only are these methods useful for obvious departures from parametric assumptions (e.g., normality) and small sample sizes, but they are also more robust than their parametric counterparts in the presences of…

Behavioral scientists often wish to determine if a sample has been taken from a symmetric population. Similarly, classroom teachers are interested in symmetry if they wish to grade on a "curve." Previously, the sign test, the Wilcoxon test and the t-test have been used to test a hypothesis concerning the symmetry of a distribution of…

The power of the t, expected normal scores, Mann-Whitney U, Tukey, a modified Mann-Whitney U, and an adaptive procedure were investigated when sampling from population models empirically developed from test score distributions. The models used were selected members of the beta family. This investigation was unique in that not only did the means of…

Researchers are often in a dilemma as to whether parametric or nonparametric procedures should be cited when assumptions of the parametric methods are thought to be violated. Therefore, the Kruskal-Wallis test and the ANOVA F-test were empirically compared in terms of probability of a Type I error and power under various patterns of mean…

Questions are raised concerning differences between traditional metric multiple regression, which assumes all variables to be measured on interval scales, and nonmetric multiple regression. The ordinal model is generally superior in fitting derivation samples but the metric technique fits better than the nonmetric in cross-validation samples.…

Dunnett's procedure for comparing K-1 treatments with a control is discussed within the context of three nonparametric models: those of Kruskal-Wallis, Friedman, and Cochran. (Author/MH)

Three nonparametric alternatives to the parametric Bartlett test are presented for handling the K-sample equality of variance problem. The two-sample Siegel-Tukey test, Mood test, and Klotz test are extended to the multisample situation by Puri's methods. These K-sample scale tests are illustrated and compared. (Author/GDC)

Discusses the application of the Kolmogorov-Smirnov two-sample tests, as an alternative to the Chi-square test, for survey research problems in business education and includes a computer program written for the convenience of researchers. The two-sample test is recommended for differentiating independent distributions. (MF)

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)