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General Linear Model for a Latin Square (Graphical)

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,

Math image

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

Math image

where Yijk are observed values of the dependent variable, Math image are effects corresponding to the 4 values of factor I, Math image – of factor II, Math image – 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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