Validity of the F-ratio Test for Replicated Latin Square Designs Under Relaxed Conditions

In a replicated latin square design, the F-ratio test statistic enjoys a noncentral Fisher distribution under the assumption of i.i.d. normal errors. This paper shows that the latter distribution still holds if a certain correlation structure is introduced within the sets of errors associated with each latin square. The correlation structure is characterized by the fact that, put in form of matrices, these sets of errors have exchangeable rows and exchangeable columns.