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By Donald J. Boudreaux

Published: Saturday, Nov. 25, 2006

As the old saw goes, "If you torture the data long enough, they'll confess."

For anyone who works with statistics, this observation rings true. It's not that data lie (although instances of outright falsification are not unknown). Rather, the problem is that even truthful statistics can be defined, arranged and interpreted in so very many different ways.

The lessons drawn from one arrangement of the data might seem crystal clear -- until an alternative arrangement of the same data is presented to tell a different story.

Here's an example: Go back to 1977, the year America began its current string of annual trade deficits, and look at what's happened since then to manufacturing employment as a percentage of total U.S. employment.

You'll see that since that year the percent of manufacturing jobs in the U.S. has steadily declined. Today it's about half of what it was 30 years ago. It appears as if trade deficits cause, or are at least associated with, declining jobs in manufacturing industries.

This appearance, though, is illusory. While the percentage of Americans today employed in manufacturing occupations is indeed about half of what it was in the mid-1970s (14 percent today compared with about 28 percent back then), the decline in manufacturing jobs as a percentage of all American jobs started way back in 1945 (when it was about 44 percent of all jobs). Because for most of the period between the end of World War II and 1977 America ran annual trade surpluses, it is illegitimate to read the data as saying that trade deficits reduce manufacturing employment.

In fact, such deficits are irrelevant in this score.

Nevertheless, I've encountered many presentations and articles in which the consistent trade deficits of the past 30 years are accused of causing the decline, during the same time period, of manufacturing employment. Speakers and writers fool their audiences into thinking that trade deficits must reduce manufacturing employment because, hey, there it is in the data: Since 1977, we've run trade deficits and manufacturing employment has shrunk.

This false illusion is caused by what statisticians call "truncating the trend." Simply by not looking at what happened to manufacturing employment before the U.S. began to run trade deficits creates the false impression that the post-1976 downward trend in manufacturing employment is somehow caused by trade deficits.

Interpreting averages can also be tricky if you're not careful. I once heard a prominent economist argue against immigration from Latin America because his studies show conclusively that such immigration lowers the average level of education in America.

This effect of Latin American immigration on the average level of education is real: adult Latin American immigrants generally have fewer years of formal schooling than do adult native-born Americans, so when they immigrate to America our average education level falls.

But so what• A fall in the average level of education doesn't mean that a current college graduate somehow becomes less educated, or looses his diploma, simply because a less-educated immigrant moves into the country and brings down the average. A change in the average need not -- and in this case does not -- change any of the individuals whose characteristics are measured to arrive at the average.

(To drive the point home, imagine calculating the average weight of people living in your town. Suppose that this average turns out to be 190 pounds. Now suppose that several skinny marathon runners move to town, each weighing no more than 140 pounds. The average weight of people in your town will fall, even though no person's weight changes.)

The same problem with averages arises when discussing average wage rates. The average wage rate can fall even though everyone's wages rise. Here's how. Suppose that America's average wage rate is now $18 per hour. Now suppose that many low-skilled immigrants arrive and find employment here at wages higher than they could earn in their home countries. Possessing lower-than-average skills means that the wages these immigrant workers earn will likely be lower than the U.S. average -- say $10 per hour.

America's average wage rate will be pulled down even though no individual's wages fall. Indeed, it is possible for every American's wages to rise and the average still fall.

Let's be clear: A change in an average might be evidence of changes in the fortunes of the individuals who compose the group for which the average is calculated. But it need not be so.

Statistics seem like straightforward, unambiguous facts; they're not. Care is required not only in their gathering but also in your interpretation of them.



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