Analysis of Reciprocals F-test developed by Miura  is used to test the equality of Inverse Gaussian (IG) means based on the assumption of homogeneity of scale parameters. However, this method is not valid when this assumption is not satisfied. There are some methods developed for comparing the equality of the IG means under heteroscedasticity of scale parameters. In this study, the goal of this study is to compare these methods under different combinations of parameters and various sample sizes. We compare the performances of the five commonly used tests in the literature via Monte Carlo simulation study. The tests considered are analysis of reciprocals (ANORE) F-test, parametric bootstrap approach (PBA), generalized pvalue approach proposed by Tian (GPA), generalized p-value approach proposed by Shi and Lv (GPSL) and computational approach test (CAT). According to simulation results, GPSL and CAT have satisfactory type I error rates for all parameter combinations. Except for the number of groups is k=7, when the sample sizes are different and scale parameters are both different and inversely proportional, the power of GPA is higher than the other tests.