The PRINTE option in the REPEATED statement in PROC GLM generates two tests for sphericity. One test is on the transformed variables, and one is on the orthogonal components. The test applied to the orthogonal components is the one to examine. The null hypothesis it tests states that the variance-covariance matrix has a TYPE H structure (or is spherical). If the test fails to reject the null hypothesis and you decide to accept that hypothesis, then you could use the traditional univariate F tests. For an example of the univariate F tests approach for a repeated measures analysis in PROC GLM, see "Repeated Measures Analysis of Variance" in the Details section of the PROC GLM documentation. If you reject the null hypothesis, then you could use either the adjusted univariate F tests or the multivariate ANOVA tests. The two adjusted univariate tests are printed below the univariate within-subjects tests in the GLM results and are labeled G-G or H-F. There are four multivariate tests (Wilks Lambda, Pillai's Trace, Hotelling-Lawley Trace, and Roy's Greatest Root). The example titled "Repeated Measures Analysis of Variance" in the Examples section of the PROC GLM documentation provides more detailed information about the multivariate ANOVA approach to repeated measures analysis in PROC GLM.

Note that for repeated measures analysis, PROC MIXED is recommended rather than either the univariate or multivariate approach using PROC GLM. PROC MIXED uses a univariate approach to repeated measures analysis and offers greater flexibility in modeling the correlations in repeated measures data. For more information, see the PROC MIXED documentation and refer to usage note 22588 and usage note 22913 for information on related topics.

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