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Is there any data analysis that can be performed on both paired and independent data? For example, we have scores on a questionnaire for individuals who were exposed and not exposed (control) to a particular disease, these are independent of one another. However, we also have pre/post data for individuals (they were given questionnaire before being exposed to the disease and after being exposed). I know this is a weird design but it is what we have to work with. My question is do we have to analyze the pre/post and independent samples separately (using paired and independent t tests respectively) or can we combine them together and perform some analysis? Combining them together is preferred because of the fact that we have a very low sample size. For example we would add the pre group with the non-exposed group (because the pre group wasnt exposed) and the post group with the exposed group (because the post group was exposed). What data analysis could you do here?

I found a paper (Derrick, Russ, Toher and White (2017)) that covers this case of partially overlapping data for normal data. However, what would you do if your data didn't meet the normality assumption?

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  • $\begingroup$ Nope. Different question. $\endgroup$ – Ryan Sep 12 '19 at 17:13
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You have a missing data problem. The people who are only measured at one time have missing data at the other time. Missing data problems are typically solved (by me, anyway) with either multiple imputation or methods that use full information maximum likelihood (mixed models or structural equation models).

You need to make an assumption that the data are either missing at random or missing completely at random. (Which, sadly, is not very testable).

The more highly the pre- and post-scores are correlated, the better you are able to get estimates of the parameters with missing data.

There are lots of resources out there, I happen to know of one, because I was involved in it: https://www.rand.org/pubs/external_publications/EP66393.html

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  • $\begingroup$ This isn't an option considering there is substantially more unpaired data than there is paired data. $\endgroup$ – Ryan Sep 12 '19 at 17:15
  • $\begingroup$ Why does that make it not an option? $\endgroup$ – Jeremy Miles Sep 12 '19 at 19:15

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