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) FF test, which is analogous to the ANOVA FF test for the normal distribution. In this article, the concept of generalized PP-value, introduced by Tsui and Weerahandi [1989. Generalized PP-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.