Mauchly's test is significant. Greenhouse-Geisser or Huynh-Feldt?

Sphericity has been violated in your repeated-measures ANOVA. You need a correction, and which one depends on a number your output already contains.

What sphericity means

That the variances of the differences between every pair of within-subject conditions are equal. With only two levels it is met automatically. With three or more it often is not, particularly when later time points drift apart.

Violating it inflates your Type I error rate: the uncorrected F-test reports more significant results than it should.

Which correction

Look at the epsilon value in your output.

- Epsilon below 0.75: use Greenhouse-Geisser. It is more conservative and appropriate when the violation is substantial. - Epsilon above 0.75: use Huynh-Feldt. Greenhouse-Geisser is considered overly conservative in this range and costs you power unnecessarily.

Some authors apply Greenhouse-Geisser throughout for consistency. That is defensible. What is not defensible is choosing after seeing which gives you a significant result.

Compute it per effect

In a factorial repeated-measures design, sphericity applies separately to each within-subject effect. A single correction applied to the whole model is wrong. Each effect gets its own epsilon and its own adjusted degrees of freedom.

How to report it

Mauchly's test indicated a violation of sphericity for the main effect of time, χ²(2) = 9.31, p = .010, so Greenhouse-Geisser corrected values are reported (ε = .68). There was a significant effect of time, F(1.36, 40.87) = 12.44, p < .001, ηp² = .29.

The fractional degrees of freedom are the correction. Report them as they come.

In Plotara

Mauchly's test runs with repeated-measures ANOVA, and Greenhouse-Geisser is computed per effect rather than once for the model.