An Application of Free Latin Squares to the Design of Experiments

10.6186/IJIMS.2017.28.2.2

Miguel G. Palomo；Francisco Ballesteros

ANOVA ； experimental design theory ； free Latin square ； hypothesis testing ； Latin square ； randomized block design

International Journal of Information and Management Sciences

28卷2期（2017 / 06 / 01）

83 - 97

英文

Free Latin squares are combinatorial objects that generalize Latin squares. In this paper we compare both objects, as designs of an experiment that use the method of Analysis of Variance (ANOVA).We show how free Latin square designs create more efficient experiments in certain cases and require fewer initial assumptions for their application. For the sake of the comparison, we begin with a detailed description of a hypothetical experiment that uses a Latin square. This is followed by another example, this time using a free Latin square design. We conclude by generalizing the use of free Latin squares in experiment design by determining a set of relevant parameters.

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