Some Thoughts Regarding the Sensitivity of t to Error in Estimated Within-Group Variance

A. J. Riopelle (2003) has eloquently demonstrated that the null hypothesis assessed by the t test involves not only mean differences but also error in the estimation of the within-group standard deviation, s. He is correct in his conclusion that the precision of the interpretation of a significant t and the null hypothesis tested is complex, particularly when sample sizes are small. In this article, the author expands on Riopelle's thoughts by comparing t with some equivalent or closely related tests that make the reliance of t on the accurate estimation of error perhaps more salient and by providing a simulation that may address more directly the magnitude of the interpretational problem.