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

_{}