Hello. I'm performing a repeated-measures ANOVA in SPSS. The Mauchly's sphericity test suggested the sphericity assumption was met (p=0.15). However, the epsilon values for Greenhouse-Geisser (GG) and Huynh-Feldt (HF) are different from 1 (0.59 and 0.77, respectively). It's supposed that I should use the "Sphericity assumed" row, but I'm worried about such low epsilon values (especially for the important change on p-values, e.g., 0.025 vs. 0.072 for GG vs. 0.051 for HF). I found some authors suggest to use GG correction if epsilon is lower than 0.75; otherwise, use HF correction. What do you suggest?
Thanks a lot.
If the G-G epsilon is less than .75, a multivariate analysis (MANOVA) provides a more powerful test.
See:
Hatcher, L. & Stepanski, E.J. (1994). A Step-by-Step Approach to Using the SAS® System for Univariate and Multivariate Statistics, Cary, NC: SAS Institue Inc., p 326.
The multivariate ANOVA has an advantage over the univariate test in that it requires no assumption of sphericity.
In selecting a test statistic, it is always desirable to choose the most powerful test. In many situations, the univariate (repeated measures) ANOVA is more powerful than the MANOVA and is therefore the better choice. However, the test to determine if the assumption of sphericity has been met is not very powerful with a small n. Therefore, only when the n is large (about 20 greater than the number of treatment levels) does the test for sphericity have sufficient power.
See:
Hatcher, L. & Stepanski, E.J. (1994). A Step-by-Step Approach to Using the SAS® System for Univariate and Multivariate Statistics, Cary, NC: SAS Institue Inc.
On pages 326-327, the authors argue that the choice between a MANOVA and a repeated measures ANOVA is a sort of catch-22: with a small n there is no certainty that the assumptions underlying the univariate (repeated measures) ANOVA have been met; with a large n the MANOVA is equally if not more powerful.
This statement is wrong:
" sphericity assumption is met (p>0.05) "
It just means that your data is not sufficient to detect a (more or less particular kind of) violation with sufficient confidence.
What you did is to take "absence of evidence" as "evidence of absence", what may be a quite common thing done but what yet is illlogical.
Jos Feys Thank you for the orientation. I'm not very familiar with MANOVA, but thank you for the references.
Jochen Wilhelm, what statement do you recommend to report it?
For instance: "the data was not sufficient to reject the hypothesis of sphericity at a 5% level of significance".
But the crucial point is that this test is not giving you any relevant information you are looking for, no matter how you phrase a statement about its result. The "non-significant" result is no indication that you miss some relevant non-sphericity, and a "significant" result is also no indication that the detecable non-sphericity is of any relevance. Formal testing of hypotheses is simply useless.
PS: the differences in the p-values (0.03 vs. 0.07 vs. 0.05) is really not big, and for the statistical point-of-view not at all "important" (as you wrote). This "importance" comes only because you think that p=0.07 means something entirely different than p=0.03 (what is not the case). The problem is that you have choosen to consider the data insufficient for interpretation when p>0.05...
It is very likely that model-misspecification (e.g. missing a relevant predictor, missing interactions, wrong distribution model) has a way stronger impact on the results than sphericity correction.
Generally, if the conclusions from this model would be ground-breaking and are not backed-up by well-understood theory and/or other data, I would not dare to interpret it if the p-value was not considerably lower, like more data needed). If it is plausible and backed-up or simply not that relevant (e.g. being one of many coherent puzzle-pieces), p < 0.1 would be ok for me to go on.
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