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The question is about sphericity of repeated measures ANOVA (2 within factors)x(3 between factors). When I check for violations of the sphericity assumption Mauchly's test of sphericity gives me a Mauchly's W of 1.000, df 0, and Sig of . . Nothing. it gives me no sig. data.

Why would that be?

Natalia Giraldo Holguín
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1 Answers1

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Because there are only 2 'within' factors. The test looks for variation in differences between levels of that factor, but when there are only two levels, there's only one relevant difference, leaving no remaining degrees of freedom to estimate any variation. Consequently things break.

Here's an example, pilfered from the wiki entry on the test.

Start with three levels of treatment applied to each patient, and consider the variation in the differences between them

           Treatments     Treatment differences
Patient    A    B    C    A−B  A−C   B−C
      1   30   27   20      3   10     7
      2   35   30   28      5    7     2
      3   25   30   20     -5    5    10
      4   15   15   12      0    3     3
      5    9   12    7     −3    2     5

Variance:                  17   10.3  10.3

Mauchly's test tests whether the 17, 10.3, and 10.3 are all plausibly generated from a single true variance (the null hypothesis) rather than possibly different ones.

But consider the same situation with only A and B levels to the treatment:

           Treatments    Treatment differences
Patient    A    B        A−B  
      1   30   27          3 
      2   35   30          5 
      3   25   30         −5 
      4   15   15         12 
      5    9   12          7 

Variance:                 17

Is 17 plausibly the result of a single true variance? Yup! But trivially so, because even if there would have been variation across treatment levels, without more levels we can't estimate it what it would have been.

conjugateprior
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