Using trimmed means to compare K measures corresponding to two independentgroups

Consider two independent groups with K measures for each subject. For the j (th) group and k(th) measure, let mu (tjk) be the population trimmed mean, j = 1, 2; k = 1,..., K. This article compares several methods for testing H -0 : mu (t1k) = mu (t2k) such that the probability of at least one Type I e rror is alpha, and simultaneous probability coverage is 1 - alpha when comp uting confidence intervals for mu (t1k) - mu (t2k). The emphasis is on K = 4 and alpha = .05. For zero trimming the problem reduces to comparing means , but it is well known that when comparing means, arbitrarily small departu res from normality can result in extremely low power relative to using say 20% trimming. Moreover, when skewed distributions are being compared, conve ntional methods for comparing means can be biased for reasons reviewed in t he article. A consequence is that in some realistic situations, the probabi lity of rejecting can be higher when the null hypothesis is true versus a s ituation where the means differ by a half standard deviation. Switching to robust measures of location is known to reduce this problem, and combining robust measures of location with some type of bootstrap method reduces the problem even more. Published articles suggest that for the problem at hand, the percentile t bootstrap, combined with a 20% trimmed mean, will perform relatively well, but there are known situations where it does not eliminat e all problems. In this article we consider an extension of the percentile bootstrap approach that is found to give better results.