1. Don't Sweat the Simple Stuff (But it's not all Simple Stuff)
David A. Rowe
Middle Tennessee State University

2. Outline what is a within-subjects design?
why should I use a within-subjects design?
how do I use a within-subjects design?
the simple within-subjects ANOVA

3. Presentation available from:

4. What is a Within-Subjects Design?
repeated measures design
same subjects tested several times
same subjects tested under different experimental conditions
subjects serve as own controls

5. Example studies:
to what degree do elementary schoolchildren identify different types of sports personality as a role model?
differences in BIA readings prior to and 10, 20, and 30 minutes following ingestion of a 12-oz soda

6. Why should I use repeated measures?
Advantages:
fewer subjects needed (all subjects complete all conditions)
subjects tested in each condition are similar (same people)
more powerful (smaller error term, less unexplained variance)

7. Why are within-subjects designs more powerful?
purpose of research is to explain, understand variance (in dependent variables)
in independent groups design, only one source of explained variance (assigned treatment, group number)
in repeated measures design, another source of explained variance is subject id (correlation between Ss’ scores on the different trials)

8. Smaller error - statistical explanation
consider formula for t-test:
independent groups:
repeated measures:

9. Smaller error - example study (simple one-way RM ANOVA)
Dependent variable = strength
3 treatment conditions
3 subjects

10. Subject One (Arnold)

11. Subjects Two and Three (Charlie and The Kid)

12. Results

13. Why should I use repeated measures?
Disadvantages:
higher levels of attrition
possible carry-over, practice, fatigue or latent effects across trials
error degrees of freedom are smaller
some independent variables can not be investigated using repeated measures designs
greater number of assumptions

14. How do I use repeated measures?
counterbalance order of treatments, e.g., for 4 treatments:

15. How do I use repeated measures?
Consider underlying assumptions:
normally distributed data
independence of observations
random selection & assignment
compound symmetry (Box, 1954)
sphericity, circularity (Huynh & Feldt, 1970; Rouanet &Lépine, 1970)

16. Compound symmetry variances of treatment conditions are equal
covariances among treatments are equal
type s matrix
sufficient, but not necessary condition
if type s matrix does not exist, hypothesis test may be too liberal (critical F too small)

17. Sphericity (circularity)
Equal variances of differences between scores
s2(T1-T2)= s2(T2-T3)= s2(T1-T3)
H matrix
less restrictive than compound symmetry
rarely occurs when T>2
can use Geisser Greenhouse correction
problem: Geisser-Greenhouse may overcorrect (too conservative)

18. What to do?

19. Example Analysis 18 subjects, 4 treatment conditions 72 observations
DV = pain rating
originally analyzed using a one-way, repeated measures ANOVA
SPSS version 8.0 (reliabilities program)
also run using independent groups ANOVA (for comparison)

20. Data - Repeated Measures

21. Data - “Independent Groups”

22. Output - Descriptive Statistics

23. Output - Correlations

24. Output - Repeated Measures ANOVA

25. Output - Independent Groups ANOVA

26. Summary
within-subjects designs have specific advantages over independent groups designs
within-subjects designs also have added disadvantages
should consider whether assumptions are met (and adjust if necessary)
seek statistical advice

27. How do I use repeated measures?
seek statistical advice early:
“Seeking the advice of a statistician after the research is over is a little like conducting a post-mortem; often he can do little more than tell you what the experiment died of”
- Charles Babbage