Between vs. Within Subject Designs

Between Vs. Within Subject Designs

Statistical Nuances for the Oneway Designs:

Looking at our workshop you may remember that the linear model for an Oneway Between Groups Anova looked like:

X = m + a + e

Where:

x = your score

m = the population mean

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

e = error

For an Oneway Within Subject Design, the model looks like:

X = m + a + p + ap + e

Where:

x = your score

m = the population mean

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

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

AP = the interactions of "A" and "S"

e = error

Note the extra terms related to the subject effect (p and AP). If you refer to your statistics book, you will see that these terms lead to a new error term definition in the F-ratio. This error term is usually smaller than the error term in the Between Subject design, leading to a bigger F and more power.

Possible Problems:

So far, the repeated measures design seems like a good thing but there can be some difficulties:

1. Practice and Carryover Effects:

In our graphic, there are three conditions, B1, B2 and B3. If subjects took them in the same order, then treatment is confounded with practice. They have practiced a great deal before they got to B3, having done B1 and B2. This is a bad thing. You can avoid this by:

Counterbalancing conditions - equalizing the amount of practice - see your text for strategies. For example, you could test one person in the B1, B2, B3 order, another with B1, B3, B2, etc. until every order is tested like:

B1, B2, B3

B1, B3, B2

B2, B1, B3

B2, B3, B1

B3, B1, B2

B3, B2, B1

Another strategy would be to repeat trials twice so people are tested like

B1, B2, B3, B3, B2, B1

This would also balance practice.

However, these techniques take many subjects. Other strategies are often used instead like:

Randomizing conditions:
People get different orders that again will minimize the effect of practice. You need a fair amount of subjects for this to work.

Using designs like the Latin Square:
Latin square designs control for nuisance variables. The nuisance variables are assigned to the rows and columns of the design and the treatments to the appropriate places in the matrix. The number of subjects below is assumed to be > 2. There must be equal numbers of levels for the rows, columns and treatments. The general scheme for the design looks as follows: