Specific inference in ANOVA: From significance tests to Bayesian procedures

Whenever in a complex design inferences on separate effects are sought, the (overall) distributional assumptions of a general model are irrelevant. The specific inference approach is examined as a useful alternative to the conventional general model approach. The specific inference for a particular effect, based only on data relevant to this effect, is valid regardless of the complexity of the design. Specific inference is first discussed in terms of significance testing. It is argued that the usual ANOVA table can be regarded as a system of specific analyses, each one resting on a separate specific model in its own right. Then specific inference is discussed within a Bayesian framework. A ‘standard Bayesian ANOVA’ is suggested as a direct extension of the usual F ‐test ANOVA. Technical developments and methodological implications are outlined.