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# Discussion 3: Alternative Methods for Evaluating the Impact of Intervention

DOI link for Discussion 3: Alternative Methods for Evaluating the Impact of Intervention

Discussion 3: Alternative Methods for Evaluating the Impact of Intervention book

# Discussion 3: Alternative Methods for Evaluating the Impact of Intervention

DOI link for Discussion 3: Alternative Methods for Evaluating the Impact of Intervention

Discussion 3: Alternative Methods for Evaluating the Impact of Intervention book

## ABSTRACT

I think in principle one has to have doubts about assumptions that you can't check. I'm not quite sure which of these you can check or which you can't. In fact, I often have a great deal of trouble when I see the term "expectation." Exactly what kind of thing is it you're expecting? What worries me is that, normally, when you're dealing with statistical assumptions and you have a relatively simple framework, you can think you can separate many of the problems/assumptions in a frequency framework. Now, we Bayesians don't always want to do that, but I think it helps to be able to say what the population would be over which you take that expectation. I have a feeling that, at least for the cross-sectional data, you're thinking of taking the expectation across the group of individuals who would be considered for training. For understanding the cross-sectional, you should get rid of the t's entirely. You don't really use them. That would simplify things. HECKMAN: They provide an added degree of generality. HARTIGAN: That's exactly why I want to take it out-it's an added degree of generality. So why have it in there? HECKMAN: In some of the discussions, there are repeated cross sections. HARTIGAN: But for the problems surrounding cross-sectional studies, I don't think you need the added term t. You could check that expectation by averaging across individuals. Now I'm just wondering in this particular case how you would check an assumption by averaging the error across these individuals. Could you check that the error distribution is symmetric? HECKMAN: Anytime you can check normality, you can also test symmetry. HARTIGAN: Hang on a second. Let's just suppose that you want to test that it's normal with some estimated mean and variance one. The way you would normally do it is estimate the mean, subtract it out, and then test for symmetry. In this case you can't estimate the mean unless you assume symmetry. Here you can only estimate the mean by cockamamie calculations on polynomials. You can only estimate it when you assume symmetry. So if you go and estimate it, then go and test whether there is symmetry, you are involved in quite a circular enterprise.