Testing equality of inverse Gaussian means under heterogeneity, based on generalized test variable

The inverse Gaussian (IG) distribution is an ideal candidate for modelling positive, right-skewed data due to the fact that its inference theory and methodology bear a striking resemblance to the normal theory and methods. For testing equality of several IG means under the assumption of equal scale parameters, there exists the ANORE (analysis of reciprocal) F test, which is analogous to the ANOVA F test for the normal distribution. In this article, the concept of generalized P-value, introduced by Tsui and Weerahandi [1989. Generalized P-values in significance testing of hypotheses in the presence of nuisance parameters. J. Amer. Statist. Assoc. 84, 602-607], is applied for testing equality of several IG means for the general cases without the assumption of homogeneity. Simulation results indicate that the proposed test has excellent type I error control under both heterogeneity and homogeneity, whereas the type I error probabilities of the ANORE test can be much larger than the nominal level under heterogeneity. The proposed procedure is illustrated using two examples.