Latin, Graeco-Latin and hyper-Graeco-Latin squares are experimental designs in which all main effects are confounded with interaction effects involving two or more experimental factors. Most marketing research experiments using these designs blindly test for main effects without establishing that interaction effects are indeed not significant. This paper first shows how the presence of significant interaction effects can distort the results of experiments using Latin square-type designs. It then presents three procedures that test the assumption of insignificant interaction effects in these designs and discusses the conditions under which each method is best employed. The unique feature common to all three procedures is that they utilize the experimental data itself to test the validity of the additivity assumption. Finally, a new procedure is presented for replicated Graeco-Latin and hyper-Graeco Latin squares that unconfounds a single, major main effect from all second order interaction effects, and estimates one two-way interaction effect involving the major experimental factor of interest. Applications illustrating the usefulness of all four procedures are presented.
Kohli, Rajeev. "Assessing Interaction Effects in Latin Square-Type Designs." International Journal of Research in Marketing 5, no. 1 (1988): 25-37.
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