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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?

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    $\begingroup$ In a repeated-measures ANOVA, "subjects" is a random effect. That's why the error term for Treatments is the Treatments x Subjects interaction. $\endgroup$ – David Lane Aug 7 '17 at 4:01
  • $\begingroup$ Thank you @David Lane. What about mixed-effects models explaining more variance than repeated-measures ANOVA? $\endgroup$ – llewmills Aug 7 '17 at 10:01
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    $\begingroup$ I've always viewed repeated measures ANOVA as a mixed effect model since it has a mixture of fixed and random effects. $\endgroup$ – David Lane Aug 7 '17 at 13:39
  • $\begingroup$ So @David Lane you're saying that not only are mixed-effects models not more powerful than repeated-measures ANOVA, they are exactly the same? $\endgroup$ – llewmills Aug 7 '17 at 23:20
  • $\begingroup$ ANOVA restricts you to one random factor (subjects) whereas mixed models can have multiple random factors. $\endgroup$ – David Lane Aug 8 '17 at 1:08
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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.

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