Problems in Ratio Correlation: The Case of Deterrence Research

Abstract

Potential problems in ratio correlation cannot be resolved outside a particular substantive context. Within the context of deterrence research, several approaches are examined: the “conceptual-meaning” resolution, the Pearsonian approximation formula and null comparison, simulation techniques, decomposition into component covariances, part correlation, and the use of residual scores. A simulation experiment shows that when the terms used in the measures of certainty of imprisonment and crime rate are randomly scrambled, the resulting ratios correlate in a manner comparable to what occurs with the data in their original form. These scrambled-data correlations, however, are due purely to artifactual effects of the common term. The most useful test for the existence of this common-term artifact appears to be the technique of part correlation. With empirical imprisonment data, the part correlations are lower than the zero-order correlations, supporting the possibility that the original correlations may have been at least partially artifactual.

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