## Thursday, May 20, 2010

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### Faulty logic: Post hoc, ergo propter hoc

For the next in the series on faulty logic, we have:

#### Post hoc, ergo propter hoc

It’s a natural tendency for people to make connections between events. “When I do this, that happens.”

When I touch something hot, I get burned.
When I don’t water my house plants, they die.
When I eat that kind of mushroom, I get sick.

As we see these connections, we often make an assumption that the prior (or coincident) event caused the other. Touching my hand to a hot stove causes my hand to be burned. Failing to water my plants kills them. Eating the wrong mushrooms makes me sick. And inferring causation is a good defense: it makes me avoid touching hot things or eating bad mushrooms. Of course, it might make me avoid eating all mushrooms, depending upon my lack of exposure to other kinds, but, you know, that’s OK: overreacting, making a rash inference can sometimes be better than the alternative.

Of course, some connections turn out to be faulty. When I go to New Jersey, it rains. We certainly know that my going to New Jersey doesn’t cause the rain. Perhaps we have a case of confirmation bias, where I’m forgetting the visits to the Garden State when it’s been sunny. Or maybe I’ve been there so few times that my sample size isn’t large enough to make any inference. I know someone who won’t eat Thai food, because “Thai food makes me sick.” How many times has that person eaten Thai food? Once.

Primitive people developed superstitions in similar ways. One year, the crops were bad. The next year, they put a basket of dead birds in the middle of the field, and the everything turned out great. Therefore, placing a basket of dead birds in the field ensures a good crop.

Coincidence (or correlation) does not imply causation.

The logical fallacy of assuming that it does is called “post hoc, ergo propter hoc”, a Latin phrase meaning “after this, therefore because of this” (or the similar “cum hoc, ergo propter hoc”, “with this, therefore because of this”).

Like the primitive farmers, we continue to make assumptions of causation, sometimes casually, sometimes to support what we already believe, sometimes to grasp at an explanation for something we desperately want explained. Post hoc, ergo propter hoc (often coupled with confirmation bias) leads us to think that vaccines are harming children, that prayer works (you pray for your sports team to win, and they win; you pray for good weather, and it's a nice day), or that taking off our shoes at the airport keeps terrorists away.

Instead, it’s important that we not jump to conclusions. We should make multiple observations. We should try different sequences in various combinations. We should design studies that test our hypotheses against alternatives, and we should consider alternative explanations.

Even with all that, we might never be sure about the real causes. But we can rule some out, and we can increase our confidence in others.

Correlation

(Click to see the cartoon on the xkcd site.)