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