Advances in Decision Sciences
Volume 2011 (2011), Article ID 748580, 8 pages
http://dx.doi.org/10.1155/2011/748580
Research Article
A Nonparametric Two-Sample Wald Test of Equality of Variances
1Centre for Computer-Assisted Research Computation and Its Applications, School of Mathematical and Physical Sciences, University of Newcastle, Newcastle, NSW 2308, Australia
2Centre for Statistical and Survey Methodology, School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia
3School of Mathematical and Physical Sciences, University of Newcastle, Newcastle, NSW 2308, Australia
Received 31 August 2011; Accepted 17 December 2011
Academic Editor: YanXia Lin
Copyright © 2011 David Allingham and J. C. W. 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
We develop a test for equality of variances given two independent random samples of observations. The test can be expected to perform well when both sample sizes are at least moderate and the sample variances are asymptotically equivalent to the maximum likelihood estimators of the population variances. The test is motivated by and is here assessed for the case when both populations sampled are assumed to be normal. Popular choices of test would be the two-sample test if normality can be assumed and Levene’s test if this assumption is dubious. Another competitor is the Wald test for the difference in the population variances. We give a nonparametric analogue of this test and call it the test. In an indicative empirical study when both populations are normal, we find that when both sample sizes are at least 25 the test is nearly as robust as Levene’s test and nearly as powerful as the test.