### 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.

Original language | English (US) |
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Pages (from-to) | 101-117 |

Number of pages | 17 |

Journal | Sociological Methods & Research |

Volume | 15 |

DOIs | |

State | Published - Jan 1 1986 |

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### All Science Journal Classification (ASJC) codes

- Social Sciences (miscellaneous)
- Sociology and Political Science

### Cite this

*Sociological Methods & Research*,

*15*, 101-117. https://doi.org/10.1177/0049124186015001008

}

*Sociological Methods & Research*, vol. 15, pp. 101-117. https://doi.org/10.1177/0049124186015001008

**Using Ratio Variables to Control for Population Size.** / Firebaugh, Glenn A.; Gibbs, Jack P.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Using Ratio Variables to Control for Population Size

AU - Firebaugh, Glenn A.

AU - Gibbs, Jack P.

PY - 1986/1/1

Y1 - 1986/1/1

N2 - 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.

AB - 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.

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U2 - 10.1177/0049124186015001008

DO - 10.1177/0049124186015001008

M3 - Article

AN - SCOPUS:84965798932

VL - 15

SP - 101

EP - 117

JO - Sociological Methods and Research

JF - Sociological Methods and Research

SN - 0049-1241

ER -