Often, when testing for shift in location, researchers will utilize nonparametric statistical tests in place of their parametric counterparts when there is evidence or belief that the assumptions of the parametric test are not met (i.e., normally distributed dependent variables). An underlying and often unattended to assumption of nonparametric…

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…

This study analysed polytomous items' psychometric properties according to nonparametric item response theory (NIRT) models. Thus, simulated datasets--three different test lengths (10, 20 and 30 items), three sample distributions (normal, right and left skewed) and three samples sizes (100, 250 and 500)--were generated by conducting 20…

Standard approaches for estimating item response theory (IRT) model parameters generally work under the assumption that the latent trait being measured by a set of items follows the normal distribution. Estimation of IRT parameters in the presence of nonnormal latent traits has been shown to generate biased person and item parameter estimates. A…

Nonparametric procedures are often more powerful than classical tests for real world data, which are rarely normally distributed. However, there are difficulties in using these tests. Computational formulas are scattered throughout the literature, and there is a lack of availability of tables of critical values. This paper brings together the…

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…

A Monte Carlo study was used to examine the Type I error rates of five multivariate tests for the single-factor repeated measures model. The performance of Hotelling's T-squared and four nonparametric tests, including a chi-square and an "F" test version of a rank-transform procedure, was investigated for different distributions, sample…

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)

The Type I error and power properties of the 2x2x2 analysis of variance (ANOVA) and tests developed by McSweeney (1967), Bradley (1979), Harwell-Serlin (1989; Harwell, 1991), and Blair-Sawilowsky (1990) were compared using Monte Carlo methods. The ANOVA was superior under the Gaussian and uniform distributions. The Blair-Sawilowsky test was…

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)

Monte Carlo methods were employed to assess the relative power of the paired samples t test and Wilcoxon's signed-ranks test under ten population shapes. Results of the study indicated that: (1) each of the two statistics was more powerful than the other in given situations; (2) the power advantages of the t test under normal theory were small;…