On the use of crime rates.

• Author: Boivin, Remi

Statistics Canada is the most important provider of justice-related data. Through various publications, the organization also issues several analyses that are widely cited. One of its most anticipated publications is the annual Police-Reported Crime Statistics in Canada, (2) which presents trends for Canada, the provinces, and census metropolitan areas. Statistics Canada also releases city-level crime statistics. To make comparisons, the publication is mostly focused on a standardized measure, crime rates. However, the use of crime rates is based on several assumptions that are seldom discussed in most criminological research.

There is a long-standing tradition of using ratio variables in the social sciences. For example, it seems obvious to calculate birth and death rates to describe population growth. Similarly, crime rates have been used for over a century to estimate the level of criminal activity of places (Bollen and Ward 1979; Pearson 1897; Schuessler 1974). They are typically calculated by dividing a count of infractions (C) by the number of people living in an area (P).

The importance of controlling for population size is easy to understand because, without such control, the incidence of crime is virtually certain to be greater for the province of Quebec than, say, for Prince Edward Island. Crime is expected to occur more frequently in more populated areas (Gibbs and Erickson 1976). Thus, the effect of population size on crime is obvious and neglecting to control for it is likely to lead to incorrect conclusions.

Two strategies are frequently used to control for population size (Firebaugh and Gibbs 1985). The component method consists of introducing population size as an independent variable in multivariate analyses of crime. This method does not offer a ready-to-use descriptive measure of crime and can only be used in "complex" statistical models. By contrast, ratio variables provide an apparently valid and easily understood measure of risk. By including population size directly in the dependent variable, the ratio method also generates simplified models.

It was also found to give more precise estimates of the effects of independent variables and should even be preferred to the component method under certain conditions (Firebaugh and Gibbs 1985, 1986; Freeman and Hannan 1975).

One such condition is that both the numerator and the denominator actually measure what they are supposed to measure. Conventional crime rates (C/P) are assumed to indicate whether crime (C) is more frequent in an area, controlling for the number of potential offenders and/or victims at risk of being involved in a criminal act (P) (Gibbs and Erickson 1976). C is usually measured by official police-recorded statistics and P is traditionally measured as the number of residents in the area. However, the reliability of both C and P is often questioned.

Using population size as a measure of the number of potential offenders and/or victims

It is often assumed that population size has a trivial effect on crime (Chamlin and Cochran 2004). Yet a widely accepted "fact" of criminology is that crime is more frequent in more populated areas (e.g. Siegel 2003). The use of conventional crime rates removes the supposed confounding effects of population size, leaving space for an array of explanations. Cross-sectional research generally confirms the positive association between population size and crime (Ousey 2000). And population size remains a strong predictor of the level of violent and property crime. Using crime rates as dependent variables instead of crime counts removes a significant portion of explained variance (Chamiin and Cochran 2004). Furthermore, using either crime rates or counts--controlling for population size--has a minimal impact on other predictors (Andresen 2006) (3).

Surprisingly little has been said about the "best" denominator to calculate accurate crime rates. The issue is sometimes discussed briefly, but few authors have questioned the use of residential population (Andresen 2006, 2007, 2011; Andresen and Jenion 2010; Boggs 1965; Chamlin and Cochran 2004; Gibbs and Erickson 1976). All concerns can be summarized in one question: Is residential population a valid indicator of the number of potential offenders and/or victims in a territorial unit?

Almost half a century ago, Boggs (1965) reminded criminologists that rates should be calculated "on the basis of environmental opportunities specific to each crime category [in order to determine] whether crime targets in certain areas are exploited at higher rates than targets in other neighborhoods" (899). She argued that the denominator of any crime rate should represent the number of attractive targets available in a territorial unit. The rate of auto theft should be calculated by dividing the number of auto thefts by the number of cars, just as rates of residential burglary have to be based on the number on housing units. She also observed that crime occurrence rates and offender rates did not match perfectly and inferred that offenders exploit criminal opportunities in their neighbourhood but also elsewhere. Gibbs and Erickson (1976) followed by arguing that "for virtually any territorial unit C [the number of crimes] is not limited to crimes committed by residents" (606). They demonstrated that American cities cannot be compared using conventional crime rates because the use of residential population size ignores the fact that some cities attract large numbers of non-residents while others don't. In other words, conventional crime rates do not take into consideration that people move around and that they expose themselves to various criminal opportunities, near to and far from their home.

Despite those early observations, conventional crime rates based on residential populations were still used frequently in criminological research. Thirty years later, Andresen (2006, 2007) compared models of spatial analysis of criminal activity in Vancouver (Canada) based on three different measures of crime--crime count, residential rate, and ambient rate. Ambient rates were calculated by dividing crime counts by an estimation of how many people were present in a given area at any time of the day, any day of the year. Andresen found a moderate positive correlation between ambient population and residential population (r = 0.411; p < 0.001) because "[t]hroughout...