Multiple Range and Multiple F Tests

Abstract

Until recent years, the problem of separating means in an analysis of variance has been handled by first making a variance ratio test of homogeneity among the means, and then testing eachpair of means, with the least significant difference (LSD). Recently, many writers have called attention to the inadequacy of the LSD test and have offered alternative methods, but the methods vary and a prospective user has difficulty deciding which one to use. In this paper, the author points out the basic differences among the methods and presents extensions of the concepts of power and significance which are useful in analyzing the procedures. In general this should help the user to decide which method to use for any given problem. Finally a new multiple range test is presented which combines the best features of previously proposed tests.