X implies Y - Testing Hypotheses of Direction of Effect Using Configural Frequency Analysis

This article proposes using formal theory to specify models for confirmatory Configural Frequency Analysis (CFA). Statement calculus is used from the perspective of relevance logic. Under this perspective, patterns are identified that are 'true', that is, that are conform with a priori made statements. Among the true patterns, there also are patterns that reflect true statements although the premise is false - the well known 'ex falso sequitur quodlibet'. These patterns are considered irrelevant, because there is no substantive connection between premise and outcome. This distinction has major implications for the selection of cells to be tested in confirmatory CFA: irrelevant cells are not considered as in support of a hypothesis. This is discussed for the operators conjunction and implication. For CFA, this approach requires an additional step. After performing standard CFA, tests are performed that examine the cells that support a hypothesis and the cells that are in contradiction to the hypothesis or irrelevant. If a hypothesis is confirmed, the cells supporting it contain more cases than expected under the CFA base model. Empirical data examples are given with data from a study on the effects of intimate partner violence.