Assumptions
As with all statistical analyses, there are a number of assumptions that should be met to justify the use of this test. Violations to these assumptions can moderately to severely affect results, and often lead to an inflation of type 1 error. With the rANOVA, there are both standard univariate assumptions to be met, as well as multivariate assumptions. The univariate assumptions are as follows:
1. Normality: For each level of the within-subjects factor, the dependent variable must have a normal distribution
2. Sphericity: Difference scores computed between two levels of a within-subjects factor must have the same variance for the comparison of any two levels. (This assumption only applies if there are more than 2 levels of the independent variable)
3. Randomness: Cases should be derived from a random sample, and the scores between participants should be independent from each other.
The rANOVA also requires that certain multivariate assumptions are met because a multivariate test is conducted on difference scores. These assumptions include:
1. Multivariate normality: The difference scores are multivariately normally distributed in the population
2. Randomness: Individual cases should be derived from a random sample, and the difference scores for each participant are independent from those of another participant.
Read more about this topic: Within-group Study, Repeated Measures ANOVA
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