Journal of Applied Mathematics and Decision Sciences
Volume 7 (2003), Issue 4, Pages 187-206
doi:10.1155/S1173912603000178

Robustness to non-normality of common tests for the many-sample location problem

Azmeri Khan1 and Glen D. Rayner2

1School of Computing and Mathematics, Deakin University, Waurn Ponds VIC3217, Australia
2National Australia Bank, Australia

Copyright © 2003 Azmeri Khan 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.

Abstract

This paper studies the effect of deviating from the normal distribution assumption when considering the power of two many-sample location test procedures: ANOVA (parametric) and Kruskal-Wallis (non-parametric). Power functions for these tests under various conditions are produced using simulation, where the simulated data are produced using MacGillivray and Cannon's [10] recently suggested g-and-k distribution. This distribution can provide data with selected amounts of skewness and kurtosis by varying two nearly independent parameters.