Investigation for the robustness of significance level when the normality assumption in hypothesis tests is violated

YALÇINKAYA A., ÇANKAYA M. N., ALTINDAĞ Ö., TUAÇ Y.

Gazi University Journal of Science, vol.30, no.2, pp.247-259, 2017 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 2
  • Publication Date: 2017
  • Journal Name: Gazi University Journal of Science
  • Journal Indexes: Scopus
  • Page Numbers: pp.247-259
  • Keywords: Contaminated distribution, Hypothesis tests, Robustness, Significance level
  • Uşak University Affiliated: Yes

Abstract

Many of the test statistics which are used to test H0: θ = θ0 are constructed under a postulated model. However, when the postulated model is not correct, the true significance level α′ will be different from that of the postulated model. The significance level α 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.