One-Way Repeated Measures Analysis of Variance (Chapter 13)
- Think of the one-way RM ANOVA as an extension of the correlated-groups t test.
- Remember with the correlated-groups t-test we said that its major advantage was controlling for disturbance variables, background/personal characteristics (individual differences) that influence the DV.
- With the RM ANOVA, we again partition the total variability in DV scores into different components – but here, we’re able to separate out the individual differences from other sources of sampling error:
Sources of Variability
|
Between-subjects ANOVA |
Repeated-measures ANOVA |
|
Between |
IV (conceptually similar to SSbetween) |
|
Within |
Error (other disturbance variables) Individual Differences (in book – "across subjects") |
|
Total |
Total |
- By separating out the influence of individual differences, we’re able to get a better (i.e., smaller) estimate of sampling error for the denominator of our F ratio.
F = IV ¸ Error
- Since our estimate of sampling error is smaller, we will get a larger F ratio. This means our F test will have more power.
EXAMPLE:
- We’re interested in people’s perceptions of how positive or negative each of the following 3 media types are for children.
1. Television
2. Movies
3. Rock Music
Step 1: hypotheses (same as with between-subjects):
are not all the same (i.e., not Null)
Step 2: critical values:
- Look it up in Appendix F, based on dfiv (numerator) and dferror (denominator)
- different formulas than BS ANOVA
Step 3: compute intermediate values:
- Because we separate out the individual differences from other sources of sampling error, we have 4 sources of variation included in our summary table:
Source SS df MS F
IV
Error
Across Subjects
Total
- What is this new "Across Subjects" term? – Again, it reflects the influence of individual differences or background characteristics on the DV.
Computation of the Sums of Squares
- As with the BS ANOVA, we compute a similar set of "intermediate values"
I. 
II. 
III. 
IV. 
- These values differ a bit from the BS values because the same people are "repeated" in each group, and because we’re splitting up the "Error" and "Across Subjects" sources of variability.
- Once we compute these four values, we get our SS, then we fill in our df and the rest of the table.
Step 4: Compute the test statistic – i.e., fill in the summary table:
|
Source |
SS |
df |
MS |
F |
|
IV |
III - II |
k - 1 |
|
|
|
Error |
I + II – III - IV |
(k – 1)(N – 1) |
|
|
|
Across Subjects |
IV - II |
N - 1 |
||
|
Total |
I - II |
kN - 1 |
Step 5: Compare Fobs to Fcrit – reject or not reject H0 ?
