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,

B C D A C D A B D A B C A B C D

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

Yijk = ai + bj + gk + eijk;

where Y_ijk are observed values of the dependent variable, a_i, i=1,4 are effects corresponding to the 4 values of factor I, b_j - of factor II, g_k - of factor III, e_ijk 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.

If the symbols do not display properly, try
the graphic version of this page

Browse Other Glossary Entries