Journal of Applied Mathematics and Decision Sciences 
Volume 8 (2004), Issue 4, Pages 235-246
doi:10.1155/S117391260400015X

Robustness to non-normality of various tests for the one-sample location problem

Michelle K. McDougall1 and Glen D. Rayner2

 1School of Information Technology, Deakin University, Waurn Ponds, VIC 3217, Australia
2Institute of Mathematical Modelling and Computional Systems, University of Wollongong, NSW 2522, Australia

Abstract

This paper studies the effect of the normal distribution assumption on the power and size of the sign test, Wilcoxon's signed rank test and the t-test when used in one-sample location problems. Power functions for these tests under various skewness and kurtosis conditions are produced for several sample sizes from simulated data using the g-and-k distribution of MacGillivray and Cannon [5].