# Repeated measures ANOVA: Mauchly's test undefined

by praznin   Last Updated June 13, 2019 07:19 AM

I'm doing a two-way between-within ANOVA in SPSS. I have two groups with 9 subjects each (so total = 18), and 24 levels of one repeated measure.

I understand why Mauchly's test of Sphericity has no meaning when there are are only 2 levels of a repeated measures factor, but I notice (using General Linear Model.....repeated measures in SPSS) that Mauchly's test of Sphericity also appears to be undefined (or gives the useless output of Mauchly's W = '.0' , p = '.') when the number of levels of a repeated measure is equal to or greater than the number of cases (subjects). In these instances, even though Mauchly's statistic is not calculated, Greenhouse-Geisser, Huynh-Feldt, and Lower-Bound Epsilon values are calculated.

I would be really happy if someone could provide some insight on why Mauchly's statistic is not calculated in these cases and what should be done to assess sphericity in the absence of Mauchly's statistic.

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In simple terms, one of the assumptions of a RM anova is that all the time points need to be correlated with each other to the same degree. The mauchly's tests this assumption, that all the times are related similarly.

When you have just 2 time points, you have only one correlation, between time 1 and 2. There is nothing else to compare this to, so the assumption is always met. Sphericity assumed, Greenhouse-Geisser, Huynh-Feldt, and Lower bound Epsilon values should all be the same in this case.

This is why you'd never use the Mauchly's test in a paired t-test, because they always have only 2 time points.

Greenhouse-Geisser, Huynh-Feldt, and Epsilon values should all be the same in this case.