1. Statistics for the Social Sciences
Psychology 340
Fall 2013
Tuesday, October 22
Repeated Measures Analysis of Variance (ANOVA)

2. Last Time ANOVA in research articles ANOVA structural model
Repeated Measures ANOVA
Definitional formulas
Computational formulas

3. This Time
Brief review of Repeated Measures ANOVA & Computational Forumlas
Assumptions in Repeated Measures ANOVA
Effect sizes in Repeated Measures ANOVA
Repeated Measures ANOVA in SPSS

4. Statistical analysis follows design
More than 2 scores per subject
One group
The 1 factor within groups ANOVA:
Repeated measures

5. Statistical analysis follows design
The 1 factor within groups ANOVA:
Repeated measures
More than 2 groups
One group
Matched groups
More than 2 scores per subject
- OR -
Matched samples

6. Example
Suppose that you want to compare three brand name pain relievers.
Give each person a drug, wait 15 minutes, then ask them to keep their hand in a bucket of cold water as long as they can. The next day, repeat (with a different drug)
Dependent variable: time in ice water
Independent variable: 4 levels, within groups
Drug A
Drug B
Drug C
Placebo

7. Within-subjects ANOVAMB MA MC MD
Drug A
Drug B
Drug C
Placebo 4 6 7 3 1 5 2
n = 5 participants
Each participates in every condition (4 of these)

8. Partitioning the variance
Drug A
Drug B
Drug C
Placebo 4 6 7 3 1 5 2
What is ?
The average score for each person
Between subjects variance

9. Partitioning the variance
Total variance
Stage 1
Between cond. variance
Within cond. variance
Stage 2
Between subjects variance
Error variance

10. Partitioning the variance
Now we return to
variance. But, we
call it
Means Square (MS)
Mean Squares (Variance)
Between conditions variance
Error variance
Recall:

11. Partitioning the variance
Total variance
Stage 1
Between cond. variance
Within cond. variance
Stage 2
Between subjects variance
Error variance

12. Computational Formulas
T = Group Total
G = Grand Total
P = Person Total
n = number of participants
k = number of conditions
N = number of scores
Drug A
Drug B
Drug C
Placebo
Person Totals 4 6 7 3
P1 = 20
P2 = 12 1 5 2
P3 = 12
P4 = 8
P5 = 4
TA = 10
TB = 20
TC = 25
TD = 5
n = 5
SSA = 8
SSB = 6
SSC = 10
SSD = 8
k = 4
N = 20
G = 60

13. Computational Formulas
Drug A
Drug B
Drug C
Placebo
Person Totals 4 6 7 3
P1 = 20
P2 = 12 1 5 2
P3 = 12
P4 = 8
P5 = 4
TA = 10
TB = 20
TC = 25
TD = 5
n = 5
SSA = 8
SSB = 6
SSC = 10
SSD = 8
k = 4
N = 20
G = 60

14. From Before
Drug A
Drug B
Drug C
Placebo 4 6 7 3 1 5 2

15. Computational Formulas
Drug A
Drug B
Drug C
Placebo
Person Totals 4 6 7 3
P1 = 20
P2 = 12 1 5 2
P3 = 12
P4 = 8
P5 = 4
TA = 10
TB = 20
TC = 25
TD = 5
n = 5
SSA = 8
SSB = 6
SSC = 10
SSD = 8
k = 4
N = 20
G = 60

16. From Before
Drug A
Drug B
Drug C
Placebo 4 6 7 3 1 5 2

17. Computational Formulas
Drug A
Drug B
Drug C
Placebo
Person Totals 4 6 7 3
P1 = 20
P2 = 12 1 5 2
P3 = 12
P4 = 8
P5 = 4
TA = 10
TB = 20
TC = 25
TD = 5
n = 5
SSA = 8
SSB = 6
SSC = 10
SSD = 8
k = 4
N = 20
G = 60

18. Between subjects variance
From Before
Drug A
Drug B
Drug C
Placebo 4 6 7 3 1 5 2
Between subjects variance

19. Computational Formulas
Drug A
Drug B
Drug C
Placebo
Person Totals 4 6 7 3
P1 = 20
P2 = 12 1 5 2
P3 = 12
P4 = 8
P5 = 4
TA = 10
TB = 20
TC = 25
TD = 5
n = 5
SSA = 8
SSB = 6
SSC = 10
SSD = 8
k = 4
N = 20
G = 60

20. Between subjects variance
From Before
Total variance
Stage 1
Between cond. variance
Within cond. variance
Stage 2
Between subjects variance
Error variance

21. Assumptions in Repeated Measures ANOVA
Observations within each treatment condition are independent (this is an assumption for 1-way ANOVA too)
Populations within each treatment follow a normal curve
Populations have equal variances 21

22. Effect sizes in Repeated Measures ANOVA
The effect size for ANOVA is r2
Sometimes called η2 (“eta squared”)
The percent of the variance in the dependent variable that is accounted for by the independent variable

23. Effect sizes in Repeated Measures ANOVA
The effect size for ANOVA is r2
Sometimes called η2 (“eta squared”)
The percent of the variance in the dependent variable that is accounted for by the independent variable

24. Repeated Measures ANOVA in SPSS
Let’s see how to do a repeated measures 1-factor ANOVA in SPSS
Analyze=>General Linear Model=>Repeated Measures
In the “Repeated Measures Define Factors” box, give your factor a name (if desired), and enter the number of levels (number of different treatment conditions) and click on “Add” and Click “Define”.
Choose the column labels (variable names) for the treatment conditions into the “within subjects variables” box (Highlight the column label on the left an click the arrow to move it into the box).
Under “options,” you can request descriptive statistics (e.g., to see group means)
Click OK
To read the output, look at the “Test of within-subjects effects” table. Look at the top line (“Sphericity assumed”)

25. ANOVA in Research Articles
F(3, 12) = 24.88, p < .01, η2 =
Means and standard deviations given in a table or in the text 25

26. Rest of Class
Work on homework (see handout)