With regard to Mauchly's test of Sphericity in order to assess validity of F statistic calculated for a one way repeated measures anova:

I understand why Mauchly's test of Sphericity has no meaning when there are are only 2 levels of a repeated measures factor.

However, I notice (using GLM.....repeated measures in SPSS) that Mauchly's test of Sphericity also appears to be undefined (or gives the useless output of Mauchly's W = '.' , 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 being 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.

I have noticed the question asked previously as part of other threads on this and other forums but I have never seen a response.