Measure for No Three-Factor Interaction Model in Three-Way Contingency Tables

Problem statement: For 2×2×K contingency tables, the measure is considered to represent the degree of departure from a log-linear model of No Three-Factor Interaction (NOTFI). We are interested in considering a similar measure for general I×J×K contingency tables. Approach: The present study proposed a measure to represent the degree of departure from the NOTFI model for I×J×K contingency tables. Also the approximate confidence interval for the proposed measure is given. Results: The proposed measure was applied and analyzed (1) for a 3×4×4 cross-classification data of dumping severity, hospital and operation which treat duodenal ulcer patients corresponding to removal of various amounts of the stomach and (2) for a 2×3×4 cross-classification data of experiment of animals (mouse and rat) on cancer (the tumor of leukemia and lymphoma) and tolazamide. Conclusion: The proposed measure is useful for comparing the degrees of departure from the NOTFI model in several tables.