Wednesday, 23 April 2014

Negative Correlations

Suppose that both attractiveness and talent are helpful things to becoming an actor.  Also suppose that attractiveness and talent have nothing to do with one another - they are completely independent in the population.  Finally, suppose that both are normally distributed.

If there were 1000 people in the population, their acting talent and attractiveness might look like this:


So those who are successful actors would likely be in the upper right part of that graph - those who stand above in talent and/or attractiveness.


So if we looked at those people who were actors, what relationship would we find between talent and attractiveness?


Hence the common perception that some people are successful only because of their appearance - there is actually a negative correlation between attractiveness and acting skill in those people who we would care to measure these things in even if there is no correlation between the two generally speaking.

Actors are a convenient example, but the problem is much broader.  There is no identifiable group of people on Earth that are not members of that group by some combination of characteristics.  Any characteristics which independently make you more likely to be a member of a group are going to appear to be negatively correlated in that group.  What's more, it is those characteristics that are of most interest to us to study.  We might be interested in the freethrow percentage and height of NBA players, where we would find those two things negatively correlated, but we would not compare it in university professors.

Similarly, we would be interested in studying the knowledge of subject and ability to convey that subject in university professors and once again we'd find that those things are negatively correlated, but we wouldn't look into their freethrows at all.

By the very fact that you have an interest in studying a particular feature about a particular group, you make it likely that you are skewing your perspective - otherwise you probably wouldn't be interested in the first place.

Of course if you are really interested only in the group you are studying, then the conclusions are completely real and valid.  In famous actors, attractiveness and acting ability probably are negatively correlated.  Just don't go generalizing that to the population in general.

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