General Linear Model for a Latin Square:
In design of experiment, a Latin square is a three-factor experiment in which for each pair of factors in any combination of factor values occurs only once.
Consider the following Latin Square,
where rows correspond to 4 values of factor I, columns - to 4 values of factor II, and letters to 4 values of factor III.
A general linear model for this experiment is
where Yijk are observed values of the dependent variable, ai, i=1,4 are effects corresponding to the 4 values of factor I, bj - of factor II, gk - of factor III, eijk are random variations.
Note: the Latin square is appropriate only if effects of all three factors are additive - that is, all interaction effects are zero.
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