This study investigated how population parameters representing heterogeneity of variance, skewness, kurtosis, bimodality, and outlier-proneness, drawn from normal and eleven non-normal distributions, also characterized the ranks corresponding to independent samples of scores. When the parameters of population distributions from which samples were drawn were different, the ranks corresponding to the same pairs of samples of scores inherited similar differences. This finding explains some known results concerning Type I error probabilities and the relative power of parametric and nonparametric tests for various non-normal densities. (Contains 11 figures and 5 tables.)