The expected value of mean square concept is used to determine the effects of the presence of interactions in the single Latin square design on F tests. The results indicate that as the number of random effects included in the experiment increase, more F tests are unbiased, and that some of these are valid F tests. However, when F test bias does occur it is almost always of a negative nature so that the conclusions stated are conservative ones. Positive F test bias may occur when the triple interaction is extant and when zero or one random variate is included in the experiment.