Extension of Multiple Range Tests to Group Correlated Adjusted Means

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Abstract
A method is given to use multiple range tests of differences among group (e.g., treatment) means that have heterogeneous variances and covariances. Explicit formulas are given for the general case, a covariance analysis, balanced incomplete block designs, simple and triple lattices, and partially balanced designs. These tests are explained in reference to Duncan s "New Multiple Range Test." It is shown that the case of unequal numbers of replications is a special case with zero covariances.