Sphericity

Description

If variance is equal across a number of treatments in an experiment, then the measurement is said to be 'spherical'.

In ANOVA and F-ratio calculations, it is assumed that the groups being tested are independent. If this is not the case, then the F-ratio will be inaccurate. Sphericity measures this independency by looking for relationships between variables.

Sphericity can be calculated via Mauchly's test (or Mauchly's W), which assesses the hypothesis that variances of the differences between conditions are equal. If the result of this test is significant (p < .05) then it can be concluded that some pairs of conditions are more related than others, and that the F-ratio is not reliable.

Discussion

The implication of non-sphericity is that Type 2 errors are more likely (which means power is reduced).

There are three corrections that can be used to adjust the F-ratio to be more valied and hence reduce Type 2 errors:

Greenhouse-Geisser estimate of sphericity

Huynh-Feldt estimate of sphericity

Lower-bound, lowest-possible estimate of sphericity

Each of these produces a correction factor for the F-statistic. The calculations and corrected F-ratio are all available through SPSS.

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Sphericity

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