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Why is the "sphericity assumption" in RM-ANOVA, i.e. the assumption of constant variance of difference scores, called "sphericity"?

(This question was suggested in the comments to a related question.)

The term seems more suited to describe compound symmetry, a condition in which the variances are homogeneous at each level of the factor, and in which each covariances between levels of the factor is equal to every other covariance. Compound symmetry is a sufficient but non-necessary condition for sphericity. Is the term perhaps a result of a confusion between compound symmetry and sphericity?

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user1205901 - Reinstate Monica
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1 Answers1

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The term "sphericity" arises because the contours of a normal random vector form a hyper-sphere when the elements have equal variance and are uncorrelated ---i.e., each point in the contour is the same distance from the mean.

Ben
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  • This answers the question "Why is N(0, I) distribution called spherical?" but does not really answer the question about RM-ANOVA. I think the Q about RM-ANOVA assumes that the meaning of "spherical distribution" is clear (see 3rd paragraph of the Q). – amoeba Apr 22 '18 at 08:01