Let's say I have a group (G) of 1000 individuals. I have complete knowledge of 200 demographic properties of each of them, from categorical (favorite drink) to numerical (age).
Let's say I invite them all for a tea party. A subgroup (g) of 20 people turns up.
Most probably, the 20 that turn up aren't a completely random group: Perhaps they like tea. Or perhaps they don't like staying home and watch TV. And I have a lot of data about them, so I should be able to find out what differentiates this group g from the big group G.
Is there a method of statistics (or related disciplines) that could tell me which (if any) of the demographic properties that differentiates g from G? Checking the demographic propoerties one by one, I would know how to do. But efficiently checking them all... every time I invite to tea... That's my challenge.
Even if group g is actually completely random, I would probably find a number of the demographic properties, which significantly (e.g. at alpha=0.05) differentiates group g from group G, just because the number of demographic properties are very high. So, if I find (e.g.) that group g is more into tea than group G, how can I trust my finding? Do I have to have a very low alpha value?
Group G is actually just a (finely tuned stratified) sample of a population (P) of 1 mill individuals. And I'm not actually just interested to know if the 20 tea drinkers are different from G, but if they are different from P too. Does this affect the methods I use?
Btw, my preferred tool to handle these questions are R.