Between vs. Within Subject Designs

Between Vs. Within Subject Designs

2. Assumptions for Repeated Measures Designs:

This is rather complicated for the novice. We will try to oversimplify. In repeated measures and mixed designs, one of the assumptions of the designs is basically that the correlations between the repeated variables are equal. Thus in our design, the Pearson's correlation coefficients (r) between A1 to A3 should not be different from each other. If they are different, then you increased your chance of Type I error (or reporting significance when there is none). The fancy name for this assumption is the circularity assumption. There is a fancy test for this based on evaluation of the variance-covariance matrix called the Test for Sphericity developed by Mauchley. Many programs test for this

The Second Big Design Issue:
Factorial Anovas with
Repeated Measures

When we discussed factorial anovas, you saw how important designs were that had more than one independent variable. In such a case, you could investigate the main effects of factor A, Factor B and their interaction (AB). You can do the same thing with Within subjects designs.

All Within vs. Mixed Designs

There are two issues to discuss:

All Within Designs
Will the design be an entirely Within subject design (meaning that all subjects serves in all possible conditions of the A and B variables?

Mixed Designs
Or might it be that only one variable is repeated measure and the other is a repeated measure. This logic can be applied to any number of independent variables.

The follow graphic compares the two designs in an AB two-away Anova situation.

Statistical Nuances:

Models:

· For a two-way mixed design - A x (B x S), the model would be:

X = m + a + b + p + ab + + bp + + e

Where:

x = your score

m = the population mean

a = the effect of your first IV or group Factor "A"

b = the effect of your second IV or group Factor "B"

p = the subject effect (the repetitions) - Factor "S"

AB = the interaction of "A" and "B"

BP = the interaction of "B" and "S"

e = error

· For a Two-way totally Within subject design (A x B x S), the model would be:

X = m + a + b + p + AB + AP + BP + abp + e