The Greenhouse–Geisser correction
is a statistical method of adjusting for lack of
sphericity
Sphericity is a measure of how closely the shape of a physical object resembles that of a perfect sphere. For example, the sphericity of the ball (bearing), balls inside a ball bearing determines the quality (business), quality of the bearing, ...
in a
repeated measures ANOVA. The correction functions as both an estimate of epsilon (sphericity) and a correction for lack of sphericity. The correction was proposed by
Samuel Greenhouse and
Seymour Geisser in 1959.
The Greenhouse–Geisser correction is an estimate of sphericity (
). If sphericity is met, then
. If sphericity is not met, then epsilon will be less than 1 (and the degrees of freedom will be overestimated and the F-value will be inflated).
To correct for this inflation, multiply the Greenhouse–Geisser estimate of epsilon to the degrees of freedom used to calculate the F critical value.
An alternative correction that is believed to be less conservative is the Huynh–Feldt correction (1976). As a general rule of thumb, the Greenhouse–Geisser correction is the preferred correction method when the epsilon estimate is below 0.75. Otherwise, the
Huynh–Feldt correction is preferred.
See also
*
Mauchly's sphericity test
*
Multivariate analysis of variance
In statistics, multivariate analysis of variance (MANOVA) is a procedure for comparing multivariate random variable, multivariate sample means. As a multivariate procedure, it is used when there are two or more dependent variables, and is often fo ...
(MANOVA)
References
{{DEFAULTSORT:Greenhouse-Geisser correction
Estimation methods