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Two Models for Interaction in a 3‐way Analysis of Variance With One Observation Per Cell
Author(s) -
Onukogu Ike B.,
Ama N. O.
Publication year - 1989
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710310603
Subject(s) - mathematics , variance (accounting) , interaction , extension (predicate logic) , main effect , factor (programming language) , additive function , interaction model , correlation , statistics , product (mathematics) , correlation coefficient , computer science , mathematical analysis , geometry , accounting , world wide web , programming language , business
The paper shows that three factor interaction can be represented by two different models in a 3‐way classification without replications. Each model is developed as a product of the three main effects plus the sum of the products of a main effect and a two‐factor interaction. A conditional F ‐test for non‐additivity is derived from each model. A pseudo‐correlation exists between the models and as this correlation coefficient tends to unity the models are shown to converge. Extension of the procedure to four‐factor interaction and higher is indicated.