If you are comparing the outcome in a case group (intervention group) to a control group and if that outcome is categorical like yes/no or present/absent or improved greatly/small improvement (for which you will have to decide what is great and slight improvement) then you can use a chi-square test. But if you are comparing the same intervention group before and after intervention then you would use a McNemar's test. If the outcome is continuous like a score then use t-test in the first scenario and paired t-test in the second scenario

For McNemar *, data are arranged in a contingency table with the same categories on each axis. So you have to know for each individual, e.g. Person 1 was in category A before and category B after,  Person 2 was in category B before and category B after.  You at least need to know the counts of subjects that switched from A to B, A to C, etc.  If you don't have this information then you can't use McNemar.

Overall, McNemar tests if people switched from category A to category B more than people switched from category B to category A, etc.

If you want to see if there is a _correlation_  between the two (as you said), it is a totally different hypothesis.  You would arrange the data in the same way as the McNemar test, but use a chi-square test.  In this case you are testing if someone in category A before is likely to be in category A after.

These are two totally different hypotheses, and it's easy to get confused. 

The coffee and tea example here may help. http://rcompanion.org/handbook/H_05.html#_Toc459550738 .  Here, "more popular" is analogous to "change from before to after", and "associated with" means correlation.

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* "McNemar" test is actually only for 2 x 2, tables but it can be extended to n x n tables.

I totally agree with my colleagues. I use McNemar test in addition to Kappa statistics when comparing the screening test results (positive/negative) with the gold standard (positive negative). Of course the same person undergo both tests.