Determination of the size of a balanced experiment in mixed ANOVA models using the modified approximate F-test

New theoretical and simulation results and a program for the approximate determination of the minimal size of experiments to compare levels of a fixed factor for balanced mixed classifications in the analysis of variance for cases, where no exact F-test exists are presented. If no exact F-test exists, an approximate test is in use, its denominator (degrees of freedom) d.f. are usually not known. For those d.f. a lower and an upper bound are derived to calculate bounds for the sample size. The approximate test is further used to calculate the expectation of the size of an experiment. By simulation experiments it is shown, how these results can be used to guarantee a given precision requirement.