You may find this blog post by Thom Baguley helpful.

• http://psychologicalstatistics.blogspot.com/2006/05/what-is-all-this-stuff-about.html

Neither. If there are more than 2 levels on a repeated measures factor it's sensible to assume the sphericity assumption is violated. The question is the severity of the violation. Using a correction based on epsilon is a sensible choice and will result in no correction if epsilon = 1 and the assumption is met.

Mauchly's Test is typically used in the context of repeated measures ANOVA to assess sphericity assumption (equal variances of differences between all possible pairs of within-subject conditions).

When Mauchly's sphericity test indicates a violation of the assumption of sphericity in repeated measures ANOVA, several corrections can be applied to adjust the degrees of freedom in the F-test and address the violation. Two common corrections are the Greenhouse-Geisser correction and the Huynh-Feldt correction.

Dr Amit Kumar, if you are referring to the robust F-tests by Welch (1951) and by Brown & Forsythe (1974), I do not understand why you are calling those tests multivariate and recommending them to someone who is using repeated measures ANOVA. They are alternatives to the ordinary F-test in one-way between-Ss (i.e., independent groups) ANOVA that do not assume or require homogeneity of variance. Please forgive me if I misunderstood what you wrote.

Brown, M. B., & Forsythe, A. B. (1974). The small sample behavior of some statistics which test the equality of several means. Technometrics, 16(1), 129-132.

Stable URL: https://www.jstor.org/stable/1267501

Welch, B. L. (1951). On the comparison of several mean values: an alternative approach. Biometrika, 38(3/4), 330-336.

Stable URL: http://www.jstor.com/stable/2332579

See also:

Article Comparison of ANOVA Alternatives Under Variance Heterogeneit...

PS- The post I was responding to has now been deleted.