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.
 A: 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.
A: This sounds like it can solved by two-way ANOVA: treating severity of illness as the dependent variable; then hospital as one factor; provider as another factor and probably include an interaction term.
You may also look into multivariate ANOVA if there are multiple dependent variables that you are interested in.
