Abstract

The robustness of the classical tests on means (Z, t, and F) and variances (chi square and F) was investigated by obtaining 30,000 (or, sometimes, 10,000 or 150,000) values of the test statistic under assumption-violating conditions and comparing the actual proportion of Type I errors with the proportion expected when all assumptions are met. The sampling and testing conditions investigated were: population shape (L-shape or bell-shape), relative population variance (1 or 4), sample size (8, 16, or 24), nominal significance level (.05,.01, or.001), and location of rejection region (left-tailed, right-tailed, or two-tailed). All tests on means were nonrobust under most of the investigated conditions, and one was nonrobust under all of them. Both tests on variances were extremely nonrobust under virtually all conditions. The worst nonrobustness of the one- and two-independent-sample Z and t tests rivaled or exceeded that of the notoriously nonrobust chi-square and F tests on variances.