## Centre for Statistical & Survey Methodology Working Paper Series

#### Publication Date

2011

#### Recommended Citation

Allingham, David and Rayner, John, A nonparametric two-sample wald test of equality of variances, Centre for Statistical and Survey Methodology, University of Wollongong, Working Paper 12-11, 2011.

https://ro.uow.edu.au/cssmwp/82

#### 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 F 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 R test. In an indicative empirical study when both populations are normal, we find that for moderate sample sizes the R test is nearly as robust as Levene’s test and nearly as powerful as the F test.