Box Correction

The Box correction entails multiplying e (epsilon), calculated from the formula below, by the numerator and denominator degrees of freedom for the F ratio, and then using the corrected df to obtain the probability associated with that F. This corrects for the exact amount of sphericity violation in the data. Notice that the notation here is different from the notation I was using in class. The quantity, c, in the expression below is a covariance. All quantities refer to the variance‑covariance matrix obtained from a repeated-measures data set. You will remember that a represents the number of levels of factor A.

where