I have an experiment in which participants can either make an A-, B- or C-type response. Each participant completes ten trials of the experiment. For each response a participant makes, they will receive a score of 1. After the ten trials, they will receive a score of 10 distributed across the three match types. For example, a participant might have a final score of something like 4 Type-A matches, 5 Type-B matches and 1 Type-C match.
I would like to group the participants by their response profile and then look at differences between them in terms of a different measurement.
Can I use a cluster analysis to group participants by their response profile? I'm uncertain given that the number of type-A matches a participant makes is clearly not independent of the number of type-B and C matches they make.