Some Results on the Tukey-Mclaughlin and Yuen Methods for Trimmed Means when Distributions are Skewed

In applied work, distributions are often highly skewed with heavy tails, and this can have disastrous consequences in terms of power when comparing groups based on means. One solution to this problem in the one-sample case is to use the TUKEY and MCLAUGHLIN (1963) method for trimmed means, while in the two-group case YUEN's (1974) method can be used. Published simulations indicate that they yield accurate confidence intervals when distributions are symmetric. Using a Cornish-Fisher expansion, this paper extends these results by describing general circumstances under which methods based on trimmed means can be expected to give more accurate confidence intervals than those based on means. The results cover both symmetric and asymmetric distributions. Simulations are also used to illustrate the accuracy of confidence intervals using trimmed means versus means.

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