The bias of the mle of box's degrees of freedom correction factor for correlation in anova

Approximate expressions for the mean and variance of the MLE of Box's 2-way ANOVA degrees of freedom factor are given for the case when the usual F test for column effects is appropriate even though there is correlation across columns. A simulation study is performed showing the approximations are good for a variety of numbers of rows and columns. The results confirm that the estimated degrees of freedom factor is badly biased when no factor at all should be used.