Repeated Measures ANOVA

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Presentation transcript:

Repeated Measures ANOVA Univariate Approach

Setting a Treatments/Conditions to compare N subjects to be included in study (each subject will receive only one treatment) n subjects receive trt i: an = N t time periods of data will be obtained Effects of trt, time and trtxtime interaction of primary interest. Between Subject Factor: Treatment Within Subject Factors: Time, TrtxTime

Model Note the random error term is actually the interaction between subjects (within treatments) and time

Mean & Variance Structure The middle assumption (assuming equal covariances among repeated measures on subjects) is not always realistic and can be tested and adjusted for by multivariate approach.

Obtaining Variances of Sums & Means

Variances of Other Means

Analysis of Variance

Expected Values in Analysis of Variance

Expected Mean Squares

Tests for Fixed Effects

Comparing Treatment Means

Comparing Time Means

Comparing Treatment Means @ 1 Time Approximate degrees of freedom on next slide

Approximate Degrees of Freedom (Satterthwaite)