Wednesday, December 22, 2010

'Confidence' and 'Rationality'

This post by Andrew Gelman suggests replacing "confidence interval" with "uncertainty interval" based in part on the "awkwardness of explaining that confidence intervals are big in noisy situations where you have less confidence, and confidence intervals are small when you have more confidence."

At the risk of putting words into Dr. Gelman's mouth, his concern is partly about the confusion that often comes from assigning common words specific technical meanings that are subtly different than their common usage. 'Confidence' here doesn't quite mean what people think it means.

One way of addressing that concern is finding new terms that don't have the same potential for confusion. Another is finding better ways of explaining the distinction. But the very fact that this is a concern illustrates an important difference between statisticians and economists.

Both statisticians and economists take common words and assign them specialized meanings. Of course, this is a reasonable, even necessary, process. As thinking in a field becomes more precise, language has to follow suit, which is why you can find a similar process in many other disciplines, but the difference in attitudes toward refined words seems particularly marked in these two.

Based on anecdotal but extensive evidence, statisticians (and I'm definitely guilty of this) constantly, almost compulsively, stop to point out that what we said isn't what you think we said. This is especially true for 'significance,' which often comes with a brief (and unwelcome) lecture on p-value and types of error. This is part of the culture of statistics. We are taught early and repeatedly that the distinctions we are making are important and need to be spelled out explicitly.

Compare this to the way economists (particularly a freshwater economists) tend to use terms like 'rational.' When economists say an actor is rational, they mean that this actor's behavior can be modeled using a simple but highly restrictive set of assumptions. Many behaviors that qualify as rational in the common sense of the term fail to meet these assumptions while more than a few behaviors that do qualify would strike most people as irrational.

But unlike statisticians, economists generally don't feel compelled to spell out these distinctions. You will often see economists using phrases like "Are people rational?" These phrases are occasionally followed by 'in the economics sense,' but they are seldom accompanied by an explanation of just how narrow this sense is.

When an economist says "people are rational" or (Steven Levitt's preferred variation) "people respond to incentives," most listeners tend to take away the impression that they mean "people act in ways that are generally considered rational" or "incentives can change the way people behave." These latter statements are completely reasonable. Most of us would agree with them. They are not, however, what the economist meant.

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