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Non-Additivity in Two-Way Analysis of Variance

John Mandel
Journal of the American Statistical Association
Vol. 56, No. 296 (Dec., 1961), pp. 878-888
DOI: 10.2307/2282001
Stable URL: http://www.jstor.org/stable/2282001
Page Count: 11
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Non-Additivity in Two-Way Analysis of Variance
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Abstract

In two-way classification analysis of variance situations there often exists a systematic type of row column interaction. A model is proposed in which the interaction is of the type Qiγ j where Qi is a parameter of the ith row, not necessarily associated with the main effect for rows, and γj is the main effect for column j. The analysis of data according to this model is given, including estimation and tests of significance. The model is more general than that involved in Tukey's "one degree of freedom for non-additivity" and includes the latter as a special case. The relationship between the two methods is discussed. Applications of the method to different types of problems are mentioned and a numerical example is included.

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