INVESTIGATION FOR THE ROBUSTNESS OF SIGNIFICANCE LEVEL WHEN THE NORMALITY ASSUMPTION IN HYPOTHESIS TESTS IS VIOLATED

Year 2017, Volume: 30 Issue: 2, 247 - 259, 19.06.2017

Mehmet Niyazi Çankaya , Abdullah Yalçınkaya Ömer Altındağ Yetkin Tuaç

Abstract

Many of the test statistics which used to test $H:\theta=\theta_0$ are constructed under a postulated model. However, when the postulated model is not correct, the true significance level $\alpha^{'}$ will be different than the significance level of the postulated model $\alpha$. The significance level $\alpha$ is used in the test statistic whether or not the hypothesis is rejected or not rejected, so determining the true significance level is important in the hypothesis tests. In this paper, when the normality assumption in hypothesis tests is violated, the true significance level for testing hypothesis about the location $\mu$ and scale $\sigma$ parameters under different contaminated distributions is obtained. As a result, the robustness of significance levels  is investigated.

Keywords

Contaminated Distribution, Hypothesis Tests, Robustness, Significance Level

References

• Arslan O. (2004), Family of Multivariate Generalized t Distribution, Journal of Multivariate Analysis 89, 329-337.
• Casella, G.; Berger, R. L. (2001). Statistical Inference (2nd ed.). Duxbury.
• Gui W. , Chen P.H. , Wu H. (2013), A Symmetric Component Alpha Normal Slash Distribution, Journal of Statistical Theory and Applications, Vol. 12, No. 1, 55-66.
• Lehmann E.L. (1999), Elements of Large-Sample Theory, New York, Springer-Verlag.
• Maronna, R., Martin, D., and Yohai, V. 2006. Robust Statistics:Theory and Methods, Wiley Series in Probability and Statistics.