I have carried out some research on whether awareness and knowledge of HIV had been increased on university students by giving a questionnaire to students before and after a presentation on HIV. Only 140 students completed the pre questionnaire and only 129 completed the post questionnaire after the presentation. So how is it possible to compare whether knowledge in students increased following the presentation as the numbers are unequal before and after? Could I compare the mean or mode score before and after even though the number of participants was different?

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#### Best Answer

Few approaches were suggested to you including

*t*-test for independent samples – but your samples are*not*independent,- repeated-measures ANOVA – but you are unable to link cases,
- mixed-effects model – the same problems like with ANOVA, plus you have only two groups and that is a small number for random effects.

The only one of the three that you actually can use is independent samples *t*-test since linkage between cases is not preserved. On another hand, there are three unknowns:

- is the change in scores significant?
- the unobserved scores,
- the linkage between scores.

The problem is that the samples are not independent and on another hand, without linkage the dependency was not observed. Because of that you should be more cautious with possible results. I think that what I would use is actually independent samples *t*-test, however the one that would provide more information on uncertainty about possible results – the Bayesian implementation of it. You could use Kruschke's BEST or the implementation by Rasmus Bååth (you can download it here).

However notice also another problem: if you gave *the same* test to the students than their responses would not only reflect gain in knowledge but also the fact that they already have seen the questions – so it could be boring for some to answer them for second time etc. So because of all those methodological flaws I would be *very* cautious with the results.

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