In true experiments in which sample material can be randomly assigned to treatment conditions, most researchers presume that the condition of equal sample sizes is statistically desirable. When one or more a priori contrasts can be identified which represent a few overriding experimental concerns, however, allocating sample material unequally will lead to more powerful tests of certain hypotheses, when the assumptions underlying the analysis of variance are known to be met. The purpose of this study was to develop systematic procedures for assigning a fixed amount of sample material to treatment conditions using either of two optimality criteria: (1) the maximization of the average precision of a given set of contrasts, or (2) the equalization of precision across a set of such contrasts. On the basis of relevant literature, the squared standard error of the estimate was adopted as the appropriate measure to minimize or equalize. Algorithms were developed mathematically to achieve each of these goals under specified conditions in single factor, fixed effects, analysis of variance applications. (PN)