This paper addresses three issues related to the analysis of variance: the practical importance of heteroscedastic methods, replacing means with some other measure of location, with an emphasis on trimmed means, and the problem of how to design meaningful simulation studies. A reasonable argument is that if the variances of J independent groups are unequal, surely the means are unequal, in which case there is no worry about a Type I error. Assuming this is true, the temptation is to use the conventional F test, but this is a highly undesirable approach for several reasons described in the paper. Another practical concern is whether substantial gains in power can be achieved by switching from means to some other measure of location. It is already known that certain resistant measures of location have substantial advantages over the means when distributions are non‐normal. This paper describes a few new results related to trimmed means. Finally, when simulations are used to study the properties of a particular testing procedure, how should they be designed? In particular, which distributions should be used, and how should our choice be influenced by experience with non‐simulated data from actual studies? Also, which characteristics of a particular testing procedure need to be studied and reported? A few suggestions are made in the hope of improving upon current practice.
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Rand R. Wilcox (1995) studied this question.