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.
Dunlap
William P
WP
Department of Psychology, Tulane University, USA.
D006801:Humans; D008960:Models, Psychological; D011582:Psychological Theory; D011584:Psychology / Q000379:methods; D012680:Sensitivity and Specificity