Hi, my name is Brian Caffo and this is Mathematical Biostatistics Boot Camp 2, and today we're going to be talking about matched two by two tables. Okay, so today we're going to be talking about matched pairs data, which is basically going to be, like, the paired t-test, but only now, we're going to have binary data. So to discuss that, we'll have to talk about the subject of Dependence, then we'll go over some specific test associated with matched pairs, contingency tables. and then talk about some other details like relationships with the Cochran–Mantel–Haenszel test. So here I have some example from, some example data from Agresti's Categorical Data Analysis of Matched pairs binary data. So the the data in this case was a survey where they were asked approval or disapproval of the politician. I believe it was a prime minister, a British prime minister on two occasions. So they had a first survey, approve or disapprove, and then they had second survey, approve or disapprove, okay? So and this two by two table is a little different than some of the other ones we've studied so in this case, 794 approved on both occasions. So you, you know, every one of these 794 measurements then represents two measurements where a person, where 794 people said approve once, then approve again 150 said approve the first time and then disprove the second time, okay? So a, a, a related very common example of matched pairs data is case control data. So here we have cases in controls we have an exposure and then an unexposed group and in this case we have 27 that were exposed. that were both cases and controls, 29 that were exposed controls, and unexposed cases, and so on. So how did this data wind up being matched, since a person, for most exposures can't be both exposed and unexposed for example, you can't both smoke and not smoke. so the way this usually works is they will, say let's say this is a retrospective study, they would take the collection of cases from charts and ascertain whether they were exposed or unexposed. And then they would go find with respect to lots of demographic variables like age, and other things. very closely matched subjects, closely matched controls, and they'd ascertain whether those controls were exposed, or unexposed. So this process of matching pairs each individual observation because they were matched on all these other variables, like age and perhaps you know, other demographics. So it's different from an instance where you have a bunch of cases, and you just select a bunch of controls, and hope that they're comparable. In this case, you've made subjects directly comparable, by at least on everything that you can think of that's important, you've matched on. So here's two very common instances of Matched, binary data.
