Thursday, June 21, 2012

When no correlation tells you about a strong correlation...

Robert Wiblin summarizes a blog post at The Atlantic.  If you'll read only one but have a little more time, read the Atlantic one, it has figures and more examples of the phenomenon.

So the phenomenon is that for some kinds of observables, correlations with other observables give some interesting results.  The one that drew me in: among Republicans, favoring marijuana legalization has absolutely no correlation with favoring wealth redistribution (and there are significant numbers of Republicans on either side of these issues).  Does this mean that these two policy issues are decided in completely unrelated ways in a Republican's mind?  That would be the vanilla explanation.

But there are two things that break that explanation.  One: favoring wealth redistribution and favoring marijuana legalization are highly correlated among the population as a whole.  So does this mean the Republican party somehow attracts people for whom these issues are unrelated?  No.

Consider 4 classifications.  Let me nerd out a bit to save some typing, G means you favor grass (marijuana) legalization, R means you favor wealth redistribution.  Then ~G and ~R mean you are against these things.  Then there are 4 possibilities: you are one of (G,R), (G,~R), (~G,R), or (~G,~R).  From what we know of republicans, one might expect it to attract social conservatives who might include (~G,R) and (~G,~R) people.  One might expect it to attract economic conservatives who might include (G,~R) and (~G,~R).  Heck, there might even be a few libertarians who are probably (~G,~R).  But what of (G,R)?

The punchline is that (G,R), people who favor both marijuana legalization and wealth redistribution probably belong to a different party than the Republicans.

So there probably are plenty of connections between how people think of marijuana legalization and wealth redistribution.  And in general, these things are correlated positively.  But then when you confound (or collide) that with a third thing, identify self as Republican, you get the interesting result that G and R are uncorrelated (a mathematical result) which might lead you to conclude incorrectly that Republican's think of G and R as unrelated while non-Republicans think they are related.  In fact, each Republican probably thinks they are related, but the fact of Republicaness biases away from (G,R) strongly enough to counterbalance the expected correlation of (~G,~R).

Other fun conclusions these blogs:  1) if you want good food in a restaurant go to older restaurants that are unfashionable and otherwise unpleasant: if food and atmosphere cause a restaurant to survive than surviving restaurants with better atmosphere probably have worse food.  2) If you want to choose a good actor from among the unemployed actors, pick a not-particuarly-good-looking one, because employed actors are probably good-looking and/or attractive, leaving behind few good-looking good-actors.

If you can think of any other counter-intuitive anti-correlations, please post them here in a comment.  ESPECIALLY if exploiting the anti-correlation might make me money. :)