I'm doing a matched sample evaluation to see if there is a statistical difference in graduation rates at a college for total sample and sub-groups within the sample after a policy change intended to increase graduates. It seems to me that because it's a dichotomous, nominal depend. var., McNemar is appropriate because it's not normally distributed. Am I on the right track or is a z-test better?
I recommend against matching.
If you do not match you can use logistic regression or other multivariable methods appropriate for a binary outcome.
If you do decide to use matching, then there are models for logistic regression (and similar methods) that are appropriate for matched outcomes, either 1:1 or k:1, that is, where multiple controls are matched to each case.
Usually matching isn't worth doing unless your data collection is quite expensive, involving, for example, an extended interview process or the collection and analysis of samples of material. The special methods needed for analysis are harder to interpret as well. Don't do it unless it saves you real money.