T-test between groups while removing within group variability

Question

I'm comparing two conditions based on an outcome variable of satisfaction with group learning (scale 1-9). The first condition consists of telling 3 groups of 3 people that their group project WILL be compared to other group projects; the second condition consists of telling 3 groups of 3 people that their group project will NOT be compared to other group projects. I want to compare the conditions themselves with a t-test, but only after eliminating within-group variability.

Normally this would be a t-test where I get a mean score of the 9 individuals from each condition (i.e., 3 groups/condition * 3 people/group) and compare these. However, this will not remove the nonindependent within-group error variance expected by individuals in shared groups.

What I want instead is to create 1 composite score for each of the 6 groups (to remove variability within each group), thus having 3 composite scores per condition, and then comparing those to each other as to remove within-GROUP variability and only comparing between-CONDITION variability.

Hopefully that makes sense, I simply don't know how to do this in R. Doing a standard t.test() with paired=T does not seem to achieve the results I want (based on the information my textbook is giving me).

Any ideas?

Answer 1

Rather than doing this with a t test, you might consider doing a two way ANOVA test with the condition as one factor and the group as another factor. In your interpretation of the results you wouldn't be concerned about the group factor, instead look at a main effect on the condition factor.