Solved – Box’s test for equal covariances or Mauchly’s test of sphericity

I am writing a report on a 2 x 3 mixed study. There is ONE within IV with TWO levels and there is ONE between subjects IV THREE levels. There are two DVs.

Sample sizes for each group is 25, 25, 27.

I tried Mauchly's test but it does not produce any results. I read somewhere that you can only use that for studies with 3 or more within IVs.

So my question is do I use the Box's test and refer to the Greenhouse Geisser output?

The short answer is that problems of sphericity of variance can only arise when you have more than two levels on your within-subjects term. (Details are on the Wikipedia page about Mauchly's sphericity test)

Sphericity is a measure of variance between pairs of levels (e.g. for three levels the variance of pair difference A – B is equivalent to variance of pair difference A – C).

Hence, when there are only two levels (one pair), sphericity is not a concern as you are just estimating one difference on those two levels (and hence why SPSS doesn't calculate Greenhouse-Geisser corrected degrees of freedom).

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