# What test to use for overlapping categories

i am analyzing a surveillance tool where people could be collected by one or both methods. So it kinda looks like a Venn diagram. What test would I use to test if there's significant differences by the methods for different characteristics? The only statistical package I have access to is SAS so please recommend something that can be done in that.

Thanks.

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Please give specific detail on what sort of differences would be tested. In other words, please describe your data some more. –  rolando2 Oct 18 '11 at 23:48
Neither your question nor your data is clear... I'm guessing your cases are individual people, that two methods of surveillance were applied to every person, sometimes succeeding and sometimes failing? –  Michael Bishop Oct 19 '11 at 0:01
I've got a population of sick people who can be captured by hospital, provider or both. I want to see if things like laboratory tests, severity of illness, etc are different between the population captured by hospital and the population captured by provider. About 70% of the population are captured by both hospital and provider. –  Liane ong Oct 19 '11 at 0:08

I would focus on just those individuals captured by either the hospital or the provider but not both, and then look for differences beteen the two populations using the usual two-sample tests, such as a t-test.

As an example, consider a binary characteristic, like sex. Suppose the data were like this:

             male   female  total     percent male
prov only      58       42    100          58
hosp only      83      117    200          42
both          355      345    700          51


If we're going to compare the percent males captured by providers and hospitals, we could compare (58+355)/(100+700) to (83+355)/(200+700), but the 355/700 are in common, so I suggest just compare 58/100 to 83/200 (say, using a $\chi^2$ test). Alternatively, as suggested by whuber below, you could compare the three groups.

If the outcome is some continuous number, I'd replace the $\chi^2$ test with a t-test or ANOVA.

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This sounds legitimate, but why throw away those who used both hospital and provider (which is the bulk of the data)? It seems like comparing all three subpopulations (hospital only, provider only, both) would be of interest. Now the t-tests become (strongly) interdependent, suggesting we work within an ANOVA setting with three categories, bearing in mind that any significant differences can not be attributed to hospital vs. provider due to the self-selection that is likely going on. (But perhaps I misunderstand what "captured by provider" really means.) –  whuber Oct 21 '11 at 15:56
@whuber - Good points; I was thinking along the lines of McNemar's test. I've added an example that illustrates what I have in mind, as well as your 3-group comparison. –  Karl Oct 21 '11 at 16:12