Statistical Functions

Zimmerman, D. W., & Zumbo, B. D. (1992). Parametric alternatives to the student t test under violation of normality and homogeneity of variance. Perceptual and Motor Skills, 74, 835-844.
*Rank order tests are effective only under violations of normality; modified t-tests are far better under conditions of violated homogeneity of variance

Clinch, J. J. & Keselman, H. J. (1982). Parametric alternatives to the analysis of variance. Journal of Educational Statistics, 7, 215-231.
*Different tests were compared under various assumption violations via Monte Carlo methods; the ANOVA F test did worst, while the Brown/Forsyth method did best overall

Tomarken, A. J. & Serlin, R. C. (1986). Comparison of ANOVA alternatives under variance heterogeneity and specific noncentrality structures. Psychological Bulletin, 99, 90-99.
*ANOVA F test alternatives were compared on Type I error rates and power under variance heterogeneity; the Welch test did best in all cases except when extreme means were paired with high variances, where the Brown/Forsyth method did better

Wilcox, R. R. (1998). How many discoveries have been lost by ignoring modern statistical methods? American Psychologist, 53, 300-314.
*Many nonsignificant research results could have been significant if modern statistical methods had been used; new methods also create more accurate confidence intervals