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

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

Presentation available from: email: darowe@frank.mtsu.edu

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

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

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)

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)

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

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

Subject One (Arnold)

Subjects Two and Three (Charlie and The Kid)

Results

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

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

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)

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)

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)

What to do?

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)

Data - Repeated Measures

Data - “Independent Groups”

Output - Descriptive Statistics

Output - Correlations

Output - Repeated Measures ANOVA

Output - Independent Groups ANOVA

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

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