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Variables Have Dimensions

Variables can be unidimensional or multidimensional. The distance from Chicago to Albuquerque can be expressed in driving time or in miles, but no matter how you measure it, distance is expressed as a straight line and straight lines are one dimensional. You can see this in figure 2.1.

FIGURE 2.1.

Two ways to measure distance.

If we add Miami, we have three distances: Chicago-Miami, Chicago-Albuquerque, Albuquerque-Miami. One dimension isn’t enough to express the relation among three cities. We have to use two dimensions. Look at figure 2.2.

FIGURE 2.2.

Three points create two dimensions.

The two dimensions in figure 2.2 are up-down and right-left, or North-South and East-West. If we add Nairobi to the exercise, we’d either have to add a third dimension (straight through the paper at a slight downward angle from Albuquerque), or do what Gerardus Mercator (1512-1594) did to force a three-dimensional object (the Earth) into a two-dimensional picture. Mercator was able to project a sphere in two dimensions, but at the cost of distortion at the edges. This is why, on a map of the world, Greenland (an island of 840,000 square miles), looks the same size as China (a land mass of about 3.7 million square miles).

Height, weight, birth order, age, and marital status are unidimensional variables and are relatively easy to measure. By contrast, political orientation (being conservative or liberal) is multidimensional and is, therefore, a lot more difficult to measure. We often talk about political orientation as if it were unidimensional, with people lying somewhere along a line between strictly conservative and strictly liberal. But if you think about it, people can be liberal about some dimensions of life and conservative about others. For example, you might agree strongly with the statement that ‘‘men and women should get equal pay for equal work’’ and also with the statement that ‘‘a strong military is necessary to defend freedom in America.’’ These statements test political orientation about domestic economic policy and foreign policy—two of the many dimensions of political orientation.

Even something as seemingly straightforward as income is multidimensional. To measure the annual income of retired Americans in Florida, for example, you have to account for social security benefits, private pension funds, gifts from children and other kin, gambling winnings, tax credits, interest on savings, wages paid entirely in cash (including tips), food stamps. . . .

And don’t think it’s easier in out-of-the-way communities around the world. If you think it’s tough assessing the amount that a waitress earns from tips, try assessing the amount a family in Haiti gets from people who are working in Miami and sending money home.

In chapter 11, I’ll discuss the building of scales and how to test for the unidimensionality of variables.

 
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