I have three clusters of patients, and for each patient I have 189 binary variables which are diagnosis codes (0 indicates the patient doesn't have the diagnosis and 1 otherwise)
I want to perform comparisons between the three group and to examine if there are variables with significant difference scores between groups ( e.g if there is cluster/group with high proportion of specific diagnosis ). Which test should I use? if its chi square what is the expected value for each variable?
For the general problem of comparing three proportions, see this thread
But, why do a test? It seems to me that if you want a cluster analysis, you don't want a test on the variables that went into the clustering. You want to look at the statistics that are output by the clustering procedure. The goal of a clustering procedure is to look at how the observations (here, patients) go together and, hopefully, to gain some insight, either on that specific question (e.g. "Huh! I knew that people who had A were likely to have B, but I didn't know they were likely to have C." Or on other variables (e.g. "Huh! People who have A, B, and C are really likely to be XXX" where XXX is something other than the conditions, like a demographic variable.)
My intuition also says that this is a variation on the "Texas sharpshooter fallacy", where the guy shoots at a barn door and then paints bullseyes around the bullet holes.
