Friday, November 29, 2013

Logical Fallacies - The Ecological Fallacy

It's been a while since I've had a fallacy post, so I though it would be a good time to investigate another one.  This one is fascinating to me.  It stems from the fact that many people do not understand how aggregate statistics and individuals relate.  Suppose you find out that the average income in a neighborhood is higher than the national average.  You know someone who lives in that neighborhood.  Does that mean that it is likely that the person has a higher than average income?  If you think it does, you're the victim of an ecological fallacy.



This stems from our desire to read things from statistics into the individuals about whom the statistics refer.  Let's look at a simple example.  Two people have 32 teeth, while a third has only 24.  On average, the people have fewer than 30 teeth.  But a randomly chosen individual has a two in three chance of having more than 30 teeth.  A more complicated example is Simpson's paradox, where some property is prevalent in both of two separate groups, but is not prevalent when the two groups are combined to form one group.

Basically, we have to be careful how we apply statistics to individuals.  Averages of groups can be very dangerously inaccurate when applied to individuals of that group.

Suppose we find that some chemical in the brain is higher among teenage homosexual males than the national average for teenage males.  We have to be careful how we apply this information to individuals.  Individual teenage homosexual males may not be likely to have high levels of the chemical at all, and may even be less likely than typical teenage males.  General averages are not applicable to individuals, even as a probability.

Basically, we have to be careful how we use statistics or we can mis-use them and spread false information and ideas.

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