A revisit to testing the equality of means for several lognormal distributions

Abstract

In this paper, we propose a new test statistic for testing the equality of several lognormal means based on Score statistic. Besides the traditional chi-square approximation to Score statistic, we use a parametric bootstrap method called computational approach test (CAT). We compare the proposed tests in terms of type I error rate and power under different number of groups and sample sizes to evaluate efficiency of these tests against the existing tests in the literature. Simulation results indicate that powers of these tests are outstandingly higher compared to their competitors under all the considered cases. Although the performance of chi-square approximation of Score statistic is insufficient in small sample cases for many problems, this approximation performs quite well for our problem even in some small sample sizes. Besides, we illustrate the considered methods using both numerical example and a real data example.

KEYWORDS:

• Lognormal distribution
• parametric bootstrap
• Score statistic
• heteroscedasticity

Disclosure statement

No potential conflict of interest was reported by the authors.