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hidden variables

Ice Cream and Muggings

Feel like mugging someone?

Did you know that the sale of ice cream is strongly correlated to the number of muggings in a given locale? Could it be that consuming ice cream leads us to attack our fellow citizens? Or perhaps miscreants in our midst mug strangers to get the money to buy ice cream? We have two variables, X and Y. Which one causes which? In this case, there’s a third variable, Z, that causes both X and Y. It’s the temperature. As the temperature rises, we buy more ice cream. At the same time, more people are wandering about out of doors, even after dark, making them convenient targets for muggers.

What causes what? It’s the most basic question in science. It’s also an important question for business planning. Lowering our prices will cause sales to rise, right? Maybe. Similarly, government policies are typically based on notions of cause and effect. Lowering taxes will cause the economy to boom, right? Well… it’s complicated. Let’s look at some examples where cause and effect are murky at best.

Home owners commit far fewer crimes proportionally than people who don’t own homes. Apparently, owning a home makes you a better citizen. Doesn’t it follow that the government should promote home ownership? Doing so should result in a safer, saner society, no? Well… maybe not. Again, we have two variables, X and Y. Which one causes which? Could it be that people who don’t commit crimes are in a better position to buy homes? That not committing crimes is the cause and home ownership is the result? The data are completely tangled up so it’s hard to prove conclusively one way or the other. But it seems at least possible that good citizenship leads to home ownership rather than vice versa. Or maybe, like ice cream and muggings, there’s a hidden variable, Z, that causes both.

The crime rate in the United States began to fall dramatically in the early 1990s. I’ve heard four different reasons for this. Which one do you think is the real cause?

  1. Legalized abortion — in 1973, the Supreme Court effectively legalized abortion in the United States. Eighteen years later, the crime rate began to fall precipitously. Coincidence?
  2. The “broken windows” theory of policing — police traditionally focused on serious crime while ignoring petty crimes. In the 1980s, sociologists began to argue that ignoring petty crime sent a signal to would-be criminals that citizens will tolerate crime in a given area. Even minor crimes like broken windows could send the wrong message. Police adopted the idea and started cracking down on petty crimes. The message? If minor crimes are not tolerated, just think what they’ll do for bigger crimes!
  3. The aging population — we’re getting older. Young people commit a disproportionate number of crimes, especially violent crimes. As our nation ages, we become more sedate.
  4. The “get tough” sentencing movement — politicians in the 1980s began to sponsor legislation to “get tough” on crime by imposing longer, mandatory sentences. One result has been a dramatic rise in our prison population. (In fact, I read recently that the U.S. has 700 people incarcerated for every 100,000 citizens. In Sweden, the equivalent rate is 70 prisoners. Could it be that we’re ten times more criminal than Swedes? Swedes are blonde and they don’t commit crimes. Cause and effect, right? Perhaps we should all dye our hair blonde.)

Which of the four variables actually caused the declining crime rate in America? A lot is riding on the answer. Unfortunately, the data are so tangled up that it’s difficult to tell what causes what. But here are some rules for thinking about correlation and causation:

  • If you think X cause Y, always ask the reverse question. Is it possible that Y caused X?
  • Always look for a hidden variable, Z, that could cause both X and Y.

Actually, the only way to prove cause and effect beyond a shadow of a doubt, is the experimental method. Which leads us to our question for tomorrow: does smoking cause cancer in humans?

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