A colleague has administered a questionnaire that asked respondents to provide both before and after values and has used the paired sample t-test to check for effect of the intervention on the dependent variable. Is this appropriate? I was of the opinion that there must be two observations that must be performed before and after the intervention. Please advise
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Judging from the little information given, the procedure is correct. You have got two metric variables that stem from identical individuals. This alone makes them paired samples that are not i.i.d. and should be investigated with a method for paired samples. The i.i.d. assumption is violated and that is all that matters. Whether one questionnaire was filled in before an intervention or resembles the memory of before the intervention has no influence on statistics. That does not mean, that retrospective questionnaires are of the same scientific value as questionnaires quo ante, but that is a question of methodology, not of statistic test choice.
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$\begingroup$ Some additional details: We are interested in finding out the effects of soil testing on maize production - among other crops. Respondents provided estimated maize production before + after soil testing. To this end, I believe you have answered my question that as long as two metric variables exist from identical individuals the IID assumption is violated and thus a method of paired sample applies. $\endgroup$ Commented Jan 15, 2018 at 12:24
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1$\begingroup$ That is indeed the heart of the problem. $\endgroup$– BernhardCommented Jan 15, 2018 at 13:09