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Dangerous Power Tools

© Frank Monaldo

Paul Krugman is a professor of economics at the Massachusetts Institute of Technology. Newsweek describes him as "Nobel bound." The self-described liberal economist specializes in the economics of international trade, though he has written eloquently about income disparity. Not a quiet and demure practitioner of the "dismal" science, he does not suffer easily those he considers fools. He has pricked and deflated the balloons of intellectual and economic pretensions of many, from former Labor Secretary Robert Reich to perennial presidential candidate Patrick Buchanan.

Recently, Krugal has expressed the frustration, especially prevalent in the social sciences, that there is a split between those comfortable in expressing ideas mathematically and those who are not. He lamented:

"There are important ideas in [economics] that can be expressed in plain English, and there are plenty of fools doing fancy mathematical models. But there are also important ideas that are crystal clear if you can stand algebra, and very difficult to grasp if you can't."

In the physical sciences, the observation that there are "plenty of fools doing fancy mathematical models" is the more common problem. There are few who are genuinely worried that there are too many erudite scientists composing beautiful prose. With this preface, perhaps it will be possible to focus on the potential misuse of a mathematical tool in the social sciences.

A common tool for untangling the influences of various contributing factors to a social phenomenon is multiple linear regression. This a fancy term for assuming that the relationship between the contributing factors and the social phenomenon is linear.

A concrete example is illuminating. Assume we are attempting to explain educational achievement. One question might be "Is parental income or parental education more important?" If we measure educational achievement using the quantity y (for example a test score) and express parental income and educational levels as x1 and x2, then in multiple linear regression, we assume the relationship

y = A0 + A1 x1 + A2 x2. to be valid.

There are many packaged computer programs that will allow anyone to simply enter the data (achievement score values, parental income and educational levels) and the computer will then produce the best fit values for the coefficients A0, A1, and A2. If (after appropriate normalization) A1 is larger than A2 we might be tempted to conclude that parental income is more important than parental education. These programs will add security to our conclusions by

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