Contents
What Happens When assumption of sphericity is violated?
The violation of sphericity occurs when it is not the case that the variances of the differences between all combinations of the conditions are equal. If sphericity is violated, then the variance calculations may be distorted, which would result in an F-ratio that is inflated.
What does the assumption of sphericity imply?
The assumption of sphericity refers to the equality of variances of the differences between treatment levels. In Repeated Measures ANOVA it is a measure of the homogeneity of the variances of the differences between levels so it is quite similar to homogeneity of variance in between-groups in the univariate ANOVA.
What causes violation of sphericity?
Sphericity is the condition where the variances of the differences between all combinations of related groups (levels) are equal. Violation of sphericity is when the variances of the differences between all combinations of related groups are not equal.
Which is an ANOVA violates the assumption of sphericity?
ANOVAs with repeated measures (within-subject factors) are particularly susceptible to the violation of the assumption of sphericity. Sphericity is the condition where the variances of the differences between all combinations of related groups (levels) are equal.
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).
What are the special assumptions in repeated measures ANOVA?
In repeated measures ANOVA containing repeated measures factors with more than two levels, additional special assumptions enter the picture: The compound symmetry assumption and the assumption of sphericity.
When to use StatView instead of sphericity in RM?
If there are only 2 levels of a factor, this problem of correlation doesn’t arise; but if there are 3 or more levels you have to guard against it. StatView does not correct for sphericity violations in RM analyses. Thus you can only reliably use StatView for RM designs in which each factor has only two levels.