I have 2 proportions I want to compare. They are from the same population but at different time periods, in between which there was an intervention.
Would this call for a McNemar's test instead of chi-squared? If yes, how do we interpret the odds ratio?
Since you don't have the same people in both samples, you should use the chi-squared test. You would set it up like this:
Period 1 Period 2
yes n_y1 n_y2
no n_n1 n_n2
where n_rp is the number of people with the given response in the specified time period. At this point, I usually tell people to use the $z$-test for the difference of two proportions because I think that is conceptually clearer for people, but the $z$-test is mathematically equivalent to the chi-squared test, it's just that software will often present the output differently. So you can use the chi-squared if you prefer.
An odds ratio will work well as an effect size measure for your case. You would form it as:
$$
OR = \frac{\frac{n_{y2}}{n_{n2}}}{\frac{n_{y1}}{n_{n1}}} = \frac{n_{y2}n_{n1}}{n_{n2}n_{y1}}
$$
The standard interpretation would apply. That is, the odds of 'yes' are OR times higher in period 2 than in period 1 (cf., Odds made simple).
McNemar's test is appropriate when you have the exact same units (people in your case) in both time periods. In that case, the setup is as follows:
Period 2
Period 1 yes no prop1
yes n_yy n_yn n_y.
no n_ny n_nn n_n.
prop2 n_.y n_.n
where n_rr is the number who responded the indicated way in each time period. In this case, you want to assess if the marginal proportions are the same, but you actually do that by running a binomial test (or chi-squared with some adaptations) on the n_yn and n_ny counts. For more on how that would work, see my answers here and here.
