Abstract
Tests for fixed and random effects can be difficult to derive for nonorthogonal designs with mixed models. However, extensions of the intrablock and inter-block analyses of Balanced Incomplete Block Designs can often be obtained. Here we derive the extensions for the broad class of Group Divisible Designs. Decompositions of the design space are used to develop exact tests for fixed and random effects in the additive mixed model with random block effects. Conditions on the design which permit the standard use of the intra-block and inter-block test statistics are given. Important subclasses of Group Divisible Designs include Equireplicate Variance Balanced Block Designs and Group Divisible Partially Balanced Incomplete Block Designs with Two Associate Classes. These two subclasses are also examined. An example from the literature of an experiment on fruit trees is used to illustrate the methods.
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