Using Ratio Variables to Control for Population Size

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Abstract
This article uses Monte Carlo computer simulation to assess two alternative ways to control for population size in regression analysis. Contrary to the claim of some social scientists, regression analyses that use ratio variables to control for size (the “ratio method” of control) are not inherently inferior to those that use a separate control variable (the “component method” of control). The ratio method appears to be inferior only because comparisons of the two methods typically omit one of the terms in the ratio regression equation. When that term is added, the ratio method outperforms the component method under conditions that are often realized in social science research. Critics of ratio variables are correct, however, in claiming that measurement error in population size, the common denominator of the ratio variables, can seriously distort the results of analyses using the ratio method. But even in that circumstance it is not necessarily the case that components should be used rather than ratios because, as the simulations demonstrate, measurement error bias can be as serious for the component method as it is for the ratio method.