# Sphericity (cont...)

## Greenhouse-Geisser Correction

The Greenhouse-Geisser procedure estimates epsilon (referred to as ) in order to correct the degrees of freedom of the *F*-distribution as has been mentioned previously, and shown below:

Using our prior example, and if sphericity had been violated, we would have:

So our *F*-test result is corrected from *F* (2,10) = 12.534, *p* = .002 to *F* (1.277,6.384) = 12.534, *p* = .009 (degrees of freedom are slightly different due to rounding). The correction has elicited a more accurate significance value. It has increased the *p*-value to compensate for the fact that the test is too liberal when sphericity is violated.

## Huynd-Feldt Correction

As with the Greenhouse-Geisser correction, the Huynd-Feldt correction estimates epsilon (represented as ) in order to correct the degrees of freedom of the *F*-distribution as shown below:

Using our prior example, and if sphericity had been violated, we would have:

So our *F* test result is corrected from *F* (2,10) = 12.534, *p* = .002 to *F* (1.520,7.602) = 12.534, *p* = .005 (degrees of freedom are slightly different due to rounding). As with the Greenhouse-Geisser correction, this correction has elicited a more accurate significance value; it has increased the *p*-value to compensate for the fact that the test is too liberal when sphericity is violated.