I have one variable 'Var1' with membership data (0,1,2,3 or 4) (let's say = no education, 1 = elemtary school 2= college etc.)
I have another variable 'Var2' with test score.

I would like to know how well test score coded by Var2 is able to predict correct
membership (Var1).

Just looking at this in passing, it reminds me of bayes/contigency table style questions but with a continuous variable.

I'm fairly sure to make a prediction of the type you want you will need to establish/assume (either through sampling or from aother source) the proportion of the populations in each of your catagorical variables. However couldn't, off the top of my head, suggest the correct way of deriving a feasible and defendable model.

So if your sample is stratified and you have an artificially high number of a rare group (to enable a better estimate of the score distribution within that group) you'd need to consider the number of people in that group within the population you are predicting for.