Investigation for the Robustness of Significance Level When the Normality Assumption in Hypothesis Tests is Violated

Abstract

Many of the test statistics which are used to test H-0: theta = theta(0) are constructed under a postulated model. However, when the postulated model is not correct, the true significance level alpha' will be different from that of the postulated model. The significance level.. is used whether or not the hypothesis will be rejected. So, determining the true significance level is important in hypothesis tests. In this paper, the true significance level for testing hypothesis about location and scale parameters under different contaminated distributions is obtained when the normality assumption is violated. As a result, the robustness of significance levels is investigated.