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Which test checks whether the sphericity assumption in a repeated measures Anova is violated?
This might lead us to conclude that our data violates the assumption of sphericity. We can, however, test our data for sphericity using a formal test called Mauchly’s Test of Sphericity.
What is the assumption of sphericity?
The assumption of sphericity states that the variance of the differences between treatment A and B equals the variance of the difference between A and C, which equals the variance of the differences between A and D, which equals the variance of the differences between B and D…
How to correct for violation of sphericity in repeated measures?
Using our prior example, and if sphericity had been violated, we would have: So our F -test result is corrected from F (2,10) = 12.534, p = .002 to F (1.277,6.384) = 12.534, p = .009 (degrees of freedom are slightly different due to rounding).
Which is the best multivariate test for sphericity?
In general, Wilks’ lambda has been recommended as the most appropriate multivariate test statistic to use. While Mauchly’s test is one of the most commonly used to evaluate sphericity, the test fails to detect departures from sphericity in small samples and over-detects departures from sphericity in large samples.
Why is sphericity important in a repeated measures ANOVA?
Sphericity can be likened to homogeneity of variances in a between-subjects ANOVA. The violation of sphericity is serious for the repeated measures ANOVA, with violation causing the test to become too liberal (i.e., an increase in the Type I error rate). Therefore, determining whether sphericity has been violated is very important.
Is there an output table for Mauchly’s sphericity test?
Interpreting Mauchly’s test. Statistical software shoold not provide output for a test of sphericity for two levels of a repeated measure factor; however, some versions of SPSS produce an output table with degrees of freedom equal to 0, and a period in place of a numeric p value.