On a levene type test for equality of two variances

Abstract

Among the many tests for the equality of two population variances, a modified Levene test W50 stands out as very robust and reasonably efficient, and thus recommended in several published comparison studies. This paper points out a hidden structural problem of this test. More specifically, the power of test W50 is bounded above by a value that can be considerably smaller than 1 for some underlying distributions, no matter how different the two population variances are. In terms of the confidence set corresponding to test W50, noninformative intervals such as (0, + ∞) may occur with non-negligible probabilities for some distributions. The above problem exists for normal distributions, but is especially severe for contaminated normal distributions. Several intuitive remedies are investigated in an attempt to correct the flaw of test W50, but retain its good features such as robustness, efficiency, simplicity and asymptotic distribution-freeness. It is found that a proposed confidence interval and its corresponding test have satisfactory robustness and are more efficient than test W50. The proposed procedures are asymptotically distribution-free and have completely eliminated the hidden problem of test W50.

Keywords:

• Contaminated normal
• asymptotically distribution-free
• dispersion
• jackknife procedure
• multiple comparisons
• robustness