Journal of Applied Mathematics and Decision Sciences
Volume 8 (2004), Issue 4, Pages 235-246

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

Copyright © 2004 Michelle K. McDougall and Glen D. Rayner. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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].