The Greenhouse–Geisser correction
is a statistical method of adjusting for lack of
sphericity
Sphericity is a measure of how closely the shape of an object resembles that of a perfect sphere. For example, the sphericity of the balls inside a ball bearing determines the quality of the bearing, such as the load it can bear or the speed a ...
in a
repeated measures ANOVA
Repeated measures design is a research design that involves multiple measures of the same variable taken on the same or matched subjects either under different conditions or over two or more time periods. For instance, repeated measurements are ...
. The correction functions as both an estimate of epsilon (sphericity) and a correction for lack of sphericity. The correction was proposed by
Samuel Greenhouse
Samuel W. Greenhouse (January 13, 1918 – September 29, 2000) was an American statistician who helped to pioneer the use of statistics in epidemiology. With Seymour Geisser, he developed the Greenhouse–Geisser correction, which is now widely ...
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 sample means. As a multivariate procedure, it is used when there are two or more dependent variables, and is often followed by significance test ...
(MANOVA)
References
{{DEFAULTSORT:Greenhouse-Geisser correction
Estimation methods