Comparison of Several Independent Population Means When Their Samples Contain Log‐Normal and Possibly Zero Observations

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Abstract
Summary.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 ANOVAF‐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.