Greenhouse–Geisser correction

{{short description|Correction for lack of sphericity}}

The Greenhouse–Geisser correction $\backslash widehat\{\backslash varepsilon\}$ is a statistical method of adjusting for lack of sphericity 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.{{cite journal |last1=Greenhouse |first1=S. W. |last2=Geisser |first2=S. |title=On methods in the analysis ofprofile data |journal=Psychometrika |date=1959 |volume=24 |pages=95–112}}

The Greenhouse–Geisser correction is an estimate of sphericity ($\backslash widehat\{\backslash varepsilon\}$). If sphericity is met, then $\backslash varepsilon\; =\; 1$. 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).{{cite book|author=Andy Field|title=Discovering Statistics Using SPSS|url=https://books.google.com/books?id=4mEOw7xa3z8C&pg=PA461|date=21 January 2009|publisher=SAGE Publications|isbn=978-1-84787-906-6|pages=461}} 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.{{cite book|author=J. P. Verma|title=Repeated Measures Design for Empirical Researchers|url=https://books.google.com/books?id=f4BsCgAAQBAJ&pg=PA84|date=21 August 2015|publisher=John Wiley & Sons|isbn=978-1-119-05269-2|pages=84}}