Greenhouse–Geisser correction

The Greenhouse–Geisser correction ${\widehat {\varepsilon }}$ 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.^[1]

The Greenhouse–Geisser correction is an estimate of sphericity ( ${\widehat {\varepsilon }}$ ). If sphericity is met, then $\varepsilon =1$ . 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).^[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]

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. p. 461. ISBN 978-1-84787-906-6.
^ J. P. Verma (21 August 2015). Repeated Measures Design for Empirical Researchers. John Wiley & Sons. p. 84. ISBN 978-1-119-05269-2.

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[1] Greenhouse, S. W.; Geisser, S. (1959). "On methods in the analysis ofprofile data". Psychometrika. 24: 95–112.

[Field2009-2] Andy Field (21 January 2009). Discovering Statistics Using SPSS. SAGE Publications. p. 461. ISBN 978-1-84787-906-6.

[Verma2015-3] J. P. Verma (21 August 2015). Repeated Measures Design for Empirical Researchers. John Wiley & Sons. p. 84. ISBN 978-1-119-05269-2.

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References