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If M yields more than one response the coefficients of each transformation sum to zero.

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If the sphericity condition is met. The sphericity condition means that the Mtransformed responses are uncorrelated and have the same variance. M´ΣM is proportional to an identity matrix, where Σ is the covariance of the Y variables.

If these conditions hold, the diagonal elements of the E and H test matrices sum to make a univariate sums of squares for the denominator and numerator of an F test. Note that if the above conditions do not hold, then an error message appears. In the case of Golf Balls.jmp, an identity matrix is specified as the Mmatrix. Identity matrices cannot be transformed to a full rank matrix after centralization of column vectors and orthonormalization. So the univariate request is ignored.
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Select Analyze > Fit Model.

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In the Construct Model Effects panel, select drug. In the Select Columns panel, select dep1. Click Cross.

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For Personality, select Manova.

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Click Run.

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Select the check box next to Univariate Tests Also.

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Time should be entered for YName, and Univariate Tests Also should be selected.
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Click OK.

The sphericity test checks the appropriateness of an unadjusted univariate F test for the withinsubject effects using the Mauchly criterion to test the sphericity assumption (Anderson 1958). The sphericity test and the univariate tests are always done using an orthonormalized M matrix. You interpret the sphericity test as follows:
The univariate F statistic has an approximate Fdistribution even without sphericity, but the degrees of freedom for numerator and denominator are reduced by some fraction epsilon (ε). Box (1954), Greenhouse and Geisser (1959), and HuynhFeldt (1976) offer techniques for estimating the epsilon degreesoffreedom adjustment. Muller and Barton (1989) recommend the GreenhouseGeisser version, based on a study of power.
The epsilon adjusted tests in the multivariate report are labeled GG (GreenhouseGeisser) or HF (HuynhFeldt), with the epsilon adjustment shown in the value column.