Error Rates and Sample Sizes for Range Tests in Multiple Comparisons

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Abstract
The problem of multiple comparisons has recently aroused a great deal of interest among statisticians. The basic F-test in an analysis of variance determines whether there is a significant difference among a group of means, but it cannot tell which means differ significantly from which others. The latter is often what the investigator really wants to know. Various multiple comparisons tests, including the range tests discussed in this paper, have been proposed. A study is made here of the error rates, a and B, and their relation to sample size, N, for three fixed range tests and three multiple range tests.