Robustness of the T Test: A Guide for Researchers on Effect of Violations of Assumptions

Abstract

The purpose of this study was to determine empirically the effects of quantified violations of assumptions underlying the t test. Using computer simulations, the effects of heterogeneity of variance, non-normality, and nonlinear transformations of scales were studied separately and in all combinations. Monte Carlo procedures were used to generate populations of scores for which distributions were normal, positively skewed, negatively skewed, and leptokurtic. Samples of varying sizes were then randomly selected from specific populations and t tests were run to identify where discrepancies between obtained and expected t distributions would occur. Results indicated that certain violations or combinations produce little distortion in resulting t distributions while other violations produce significant discrepancies. Specific guidelines and reference tables were developed to assist the researcher in assessing the severity of certain violations or degrees of violation.