The Analysis of Latin Squares with a Certain Type of Row-Column Interaction

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Abstract
A serious limitation in the use of latin squares is the confounding of the main effect of each factor with the interaction of the remaining two factors. In some cases, the interaction of rows and columns can be expressed as a multiplicative term of assigned factors associated with rows and columns. The analysis of such designs is presented in detail. An example is discussed. The method ia extended to the case where the treatment effects are linearly related to a given concomitant variable. A brief discussion is given of the relation of the proposed method with other tests for non-additivity.

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