An investigation of the robustness of the Type I error rate of the t, M-W-W, Welch and Welch on ranks tests applied to reaction time populations with unequal variances.

Abstract

This thesis investigates the robustness of the Type I error rate of the t test, the t test on ranks (Mann-Whitney-Wilcoxon), the Welch test and the Welch test on ranks applied to reaction time populations with unequal variances. Reaction time is often encountered as a dependent variable in educational and behavioural research. Reaction time data are typically skewed and are commonly modelled on a family of distributions known as the ex-Gaussian. A Monte Carlo study compared the robustness of type I error rates of the four tests under study under 36 conditions wherein four factors were observed: total sample size ($N=24$ and 72), ratio of sample sizes ($n\sb1:n\sb2$ = 1:1, 1:2, and 1:3); ratio of population variances (var1:var2 = 1:1, 1:2, 1:4, and 1:9), and negative and positive conditions. In each condition, 5,000 scores were generated from Miller's (1988) most skewed distribution that represented a boundary condition of reaction time data. The results indicated that the t test was the preferred option under all simulated conditions, except the negative condition. Furthermore, under the negative condition, all four tests produced liberal Type I errors.