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How do assumptions of sphericity differ from assumptions of homogeneity of variance?
I believe sphericity refers to equality in variance across the different repeated measures, whereas homogeneity of variance (assuming that is what you’re asking about) refers to homogeneity of variance in the dependent variables in a single measure across different levels of the independent variables.
How do you assume 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…
Is sphericity and homogeneity of variance the same?
Sphericity is the condition where the variances of the differences between all combinations of related groups (levels) are equal. Sphericity can be likened to homogeneity of variances in a between-subjects ANOVA.
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.
Can a one way ANOVA be used to check for normality?
In general, a one-way ANOVA is considered to be fairly robust against violations of the normality assumption as long as the sample sizes are sufficiently large. Also, if you have extremely large sample sizes then statistical tests like the Shapiro-Wilk test will almost always tell you that your data is non-normal.
How does sphericity relate to the repeated measures factor?
Basically, sphericity refers to the equality of the variances of the differences between levels of the repeated measures factor. In other words, we calculate the differences between each pair of levels of the repeated measures factor and then calculate the variance of these difference scores.
Is the sphericity assumption necessary for the F-test?
However, it is not a necessary condition. The sphericity assumption is a necessary and sufficient condition for the F-test to be valid; it states that the within-subject “model” consists of independent (orthogonal) components.