ANOVA Assumptions
When running an analysis of variance to analyse a data set, the data set should meet the following criteria:
(1) Normality: scores for each condition must be normally distributed around their mean.
(2) Homogeneity of variance: each population must have the same error variance.
(3) Sphericity of the covariance matrix: ensures the F ratios match the F distribution
For the between-subject effects to meet the assumptions of the analysis of variance, the variance for any level of a group must be the same as the variance for the mean of all other levels of the group. When there is homogeneity of variance, sphericity of the covariance matrix will occur, because for between-subjects independence has been maintained.
For the within-subject effects, it is important to ensure normality and homogeneity of variance are not being violated.
If the assumptions are violated, a possible solution is to use the Greenhouse & Geisser or the Huynh & Feldt adjustments to the degrees of freedom because they can correct for issues that can arise should the sphericity of the covariance matrix assumption be violated.
Read more about this topic: Mixed-design Analysis Of Variance
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