Comparison of several independent population means when their samples contain log-normal and possibly zero observations

In this paper, we consider the problem of testing the mean equality of several independent populations that contain log-normal and possibly zero observations. We first showed that the currently used methods in statistical practice, including the nonparametric Kruskal-Wallis test, the standard ANOVA F-test and its two modified versions, the Welch test and the Brown-Forsythe test, could have poor Type I error control. Then we propose a likelihood ratio test that is shown to have much better Type I error control than the existing methods. Finally, we analyze two real data sets that motivated our study using the proposed test.