Group-Theoretic Reduction of Latin Squares in Experimental Designs

A Latin square or Latin square design is an experimental design that controls nuisance factors by blocking them off in two directions in order to study the effect of a treatment variable. It is produced when each treatment appears once and only in each row and column of the square. In this study, group theory concepts are used to determine the subgroup of a group-structural Latin squares that would represent the original Latin square with minimal efficiency loss. Latin square of the order 6x6 to 12x12 that have group structures were considered. The largest subgroup for each Latin Square was determined by finding the maximal normal subgroup of the given group. Results revealed that, on the average, the efficiency loss was only 6%.

 

Key words – Latin square, normal subgroup, factor group