Comparisons of Lognormal Population Means

Comparisons of two lognormal population means are investigated. For large samples, the conventional test for significance of the population means is the ordinary Student /-test with normal critical value. By Chen and Loh's result (Ann. Statist. 20 (1992)), however, the transformed i-test based on legdata is asymptotically more powerful than the ordinary i-test. In this paper, a new power transformation (hence a new transformed /-test) is proposed. The new transformed /-test is proven to be asymptotically more powerful than the one based on log-data. Both small sample and large sample properties of the proposed estimate for the power-transformation parameter are studied. A simulation study shows that the advantages of the new test over the /-test based on log-data are overwhelming and evident for sizes of the two samples as small as 20 and 30, or even 10 and 15. The simulation results also show that the new test has greater asymptotic power than Rao's efficient score test.