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…

Developed an extension of the Hollander and Sethuraman (M. Hollander and J. Sethuraman, 1978) statistic (B squared) for testing discordance among intra-block rankings of K elements for multiple groups of raters. Simulation results confirmed the usefulness of B squared as an omnibus test of interaction among intra-block ranks and demonstrated its…

Through simulation, showed that a multivariate test of interactions for aligned ranks in a split-plot design controlled Type I error rates for nonnormal data with nonspherical covariance structures. This method also performed well in the presence of a strong repeated measures main effect and demonstrated more statistical power than parametric…

Robustness and power of parametric, semi-parametric, and nonparametric tests of between-group discordance were compared in this simulation study. The empirical Type I error rates and power of nine tests were compared. When data were sampled from the any differences especially favor young women in single-sex Catholic secondary schools, and whether…

Real world data often fail to meet the underlying assumptions of normal statistical theory. Many statistical procedures in the psychological and educational sciences involve models that may include a system of statistical equations with non-normal correlated variables (e.g., factor analysis, structural equation modeling, or other complex…

C. L. Olson (1976, 1979) suggests the Pillai-Bartlett trace (V) as an omnibus multivariate analysis of variance (MANOVA) test statistic for its superior robustness to heterogeneous variances. J. Stevens (1979, 1980) contends that the robustness of V, Wilk's lambda (W) and the Hotelling-Lawley trace (T) are similar, and that their power functions…