I am interested in whether a mixed-effects model yields more power than a repeated measures ANOVA and why.
A fried of mine wrote this in an email the other day and I found it striking.
"Repeated-measures ANOVA does not account for random effects. It treats everyone in the same cell in a factorial design the same. Any residual error goes into the SS(error) hence this accounting for subject-level variance should decrease the MSerror in a mixed-effects model and increase its power over a repeated-measures ANOVA."
Is this passage true? Are mixed-effect models more powerful, and, if so, is this because they account for more of the Error variance than repeated-measures ANOVA?
Best Answer
In a repeated-measures ANOVA, "subjects" is a random effect. That's why the error term for Treatments is the Treatments x Subjects interaction. ANOVA restricts you to one random factor (subjects) whereas mixed models can have multiple random factors.