How to analyse data from the same group where some people have opted out and data is anonymous? I have a peculiar situation, I am conducting research and had a group of students participate in it. I had them scored on (property) $X$ and say $n_1$ people participated.
After an intervention, I measured the same property $X$ but this time $n_2$ (where $n_2 < n_1$) people participated.
Now the catch is that the experiment is so designed that the forms are filled in anonymously and there is no way to compare the scores of the same individual.
So now I am left with the group mean and I want to run some tests on these.
I want to know -- which tests are most suitable for this kind of data?
Please explain the rationale as well or give hints /links so that I am convinced.
 A: You have implicitly paired samples (before and after intervention) but because of anonymity, the pairing is lost.
As a result, if you want to test for a treatment effect, you're left with an independent samples two-sample test (you don't actually have complete independence because of the pairing effect, but it shouldn't matter in this case).
The most common procedures for that would be a two-sample $t$ test or a Mann-Whitney-Wilcoxon test.
At the end you say "now I am left with the group mean" -- I hope you have more information than just the group mean, or there will be nothing you can feasibly do. If you have the original scores, you should be fine to do either procedure, or if you have the means, standard deviations and sample sizes you would be able to at least do the t-test.
Both tests make some assumptions, but the main difference in the assumptions (if you're testing means) is that the t-test makes the additional assumption of normality; if your two samples are not too strongly non-normal about their own group means, this won't really matter very much, but you would want to make some assessment of the suitability of that assumption. If you're specifically testing mean-shift alternatives, you should check that the shapes and spreads are similar even if you use Wilcoxon-Mann-Whitney (it can be used without that assumption but the alternative doesn't have a location-shift interpretation any more).
