A simulation study comparing two approximations for a quasi t-quantile, used in repeated measures ANOVA.

In the analysis of variance it is not unusual to form a denominator of an approximate t-statistic from a linear combination of mean squares. Two examples include the Behrens-Fisher problem and the repeated measures analysis of variance. One solution to the problem of finding the appropriate degrees of freedom is to use Satterthwaite's approximation while another solution, due to Cochran, is to form a weighted t-statistic. Based upon computer simulations I have found that the magnitude of the bias of the Satterthwaite approximation was less than that of the Cochran approximation in 68/75 cases considered. When the bias of the Cochran approximation was smaller than the bias of the Satterthwaite approximation, I found that the estimated bias of the Satterthwaite approximation no more than 0.5 per cent in the cases considered. I recommend performing the additional calculations required for the Satterthwaite approximations when combining two mean squares, especially when one mean square is based upon 12 or fewer degrees of freedom.