Repeated Measures ANOVA

1
Repeated Measures ANOVA

• Univariate Approach

2
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

3
Model
Note the random error term is actually the
interaction between subjects (within treatments)
and time
4
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.
5
Obtaining Variances of Sums Means
6
Variances of Other Means
7
Analysis of Variance
8
Expected Values in Analysis of Variance
9
Expected Mean Squares
10
Tests for Fixed Effects
11
Comparing Treatment Means
12
Comparing Time Means
13
Comparing Treatment Means _at_ 1 Time
Approximate degrees of freedom on next slide
14
Approximate Degrees of Freedom (Satterthwaite)