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. Much sociological research consists of relating complex indexes to each other. These indexes are formed by combining separate but related indicators in some fashion, by adding, subtracting, multiplying, and dividing them in various ways. Such indexes are indispensable to many kinds of social scientific research, and it is therefore important to consider carefully the ways in which the construction of our indexes can affect the validity and interpretation of our research. This paper will consider in detail one such type of index construction: the formation of ratios, with specific attention to problems that may arise when attempting to correlate two ratios in which the numerator of one is the same as the denominator of the other. In one rapidly expanding body of research, the deterrent or preventive effects of legal sanctions on crime, the strongest findings of most of the major