A multivariate analysis of an experimental design involving a complete set of latin squares

A model for an experimental design involving a complete set of Latin squares for testing the homogeneity of treatment effects was constructed and analyzed by Gourlay. In his analysis, however, if one or both of the preliminaryF-tests are significant, the analysis cannot differentiate. He then suggests the use of a less desirable test which is biased and has fewer degrees of freedom, regardless of the number of replications (the d.f. cannot be increased by increasing the replications). Further, when heterogeneity of variance occurs, Gourlay's test procedures are in general invalid. The present paper reviews Gourlay's analysis and proposes a modified test procedure.My thanks are due to Drs. R. S. Hirsch, R. L. Erdmann, and R. M. Simons of IBM Corporation for many stimulating discussions, and to Professor D. Teichroew of Stanford University for permission to refer to his paper 6] and his assistance. I also wish to thank B. A. Snyder for correcting many linguistic mistakes.