Greenhouse–Geisser correction
The Greenhouse–Geisser correction [math]\displaystyle{ \widehat{\varepsilon} }[/math] 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.[1]
The Greenhouse–Geisser correction is an estimate of sphericity ([math]\displaystyle{ \widehat{\varepsilon} }[/math]). If sphericity is met, then [math]\displaystyle{ \varepsilon = 1 }[/math]. 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).[2] 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.[3]
See also
References
- ↑ Greenhouse, S. W.; Geisser, S. (1959). "On methods in the analysis ofprofile data". Psychometrika 24: 95–112.
- ↑ Andy Field (21 January 2009). Discovering Statistics Using SPSS. SAGE Publications. pp. 461. ISBN 978-1-84787-906-6. https://books.google.com/books?id=4mEOw7xa3z8C&pg=PA461.
- ↑ J. P. Verma (21 August 2015). Repeated Measures Design for Empirical Researchers. John Wiley & Sons. pp. 84. ISBN 978-1-119-05269-2. https://books.google.com/books?id=f4BsCgAAQBAJ&pg=PA84.
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