Black Americans are not more likely to be shot by the police than White Americans in proportion to each group's rate of interaction with the police, as measured by crime rate, a new study argues.

The report, by psychologists Joseph Cesario and David Johnson and criminologist William Terrill, analyzes trends in fatal shootings by police in 2015 and 2016 using a variety of data sources.

Measuring racial disparities in police use of force is a touchy subject. High-profile shootings of black men by police have been a focal point for Blacks Lives Matter and similar groups, which see such shootings as both endemic of larger police abuses and an epidemic in their own right.

Most analyses of the police shooting disparity compare the number of black and white people shot to each group's proportion in the population. Black people make up about 13 percent of the population, the argument goes, so should make up about 13 percent of police shootings. These analyses regularly find vast disparities between racial groups, with whites underrepresented and blacks substantially overrepresented.

The paper argues that this methodology is misguided, because it "carries with it a critical assumption: the opportunity for [police shooting] to occur is equally likely for every person within each group." In other words, black and white Americans as distinct groups are not equally likely to be in a situation where they are exposed to police force.

As such, the rates of shooting need instead to be compared to rates of police exposure. Cesario et al. propose to approximate these using crime rates. There are well-established racial disparities in crime rates; for example, black Americans account for 26 percent of all arrests, or twice their representation in the population.

The study compares data on fatal police shootings in 2015 and 2016 to three rates of crime, those for murder, violent crime, and weapons violations. The study's authors select these three crimes because, according to their research, most police use of deadly force come in violent situations: "1% of fatal shootings are by accident and almost 85% involve armed citizens." This means that these violent crime rates likely explain a majority of the situations in which police exercise deadly force.

Capturing the true rate of each crime by race is a notoriously tricky proposition, because crime by its nature is not the sort of thing one is likely to report. To address this issue, the study's authors collected stats from a number of resources, including the FBI's crime reporting system and the National Crime Victimization Survey. These, they argue, help avoid the potential pitfall of systematic racial bias in any given dataset.

So what happens when Cesario et al. benchmark police shooting rates against crime rates? Across the board, whites are more likely to be shot, almost regardless of the measure of crime rate used. Whites were more likely to be shot using each racial group's rate of homicides, violent crimes, and weapons violations, as based on multiple sources. There were only two exceptions: blacks were more likely to be shot by the police in proportion to two measures of violent crime that included those violent crimes that were "less severe."

The study also looked at the racial disparity in specific situations, namely police shootings of unarmed citizens and in situations where the person shot was thought to be "reaching for or holding an object." This latter case applies to shooting victims like Stephon Clark, whom police shot after mistaking Clark's cellphone for a gun.

In both instances, the study found at best limited evidence of systematic anti-black disparity in police shootings. In the case of unarmed citizens, "officers either showed no meaningful disparity in either direction [between white and black] or, if anything, an overall pattern of anti-White disparity."

In what the study's authors called their "most damning result," they found "nonsignificant" anti-black disparity for cases where the victim was holding an object. They are quick to caution the reader against over-interpreting this result, noting that the number of instances of police shootings involving unarmed citizens or police assuming possession of a gun are few enough that any conclusions drawn from them may not be representative.

Beyond this, the study had several significant limitations. It focuses only on national-level trends, meaning that the conclusions it draws provide only a limited insight into the relationship between race and police shootings. These conclusions do not, in other words, mean that any particular police department does not engage in racially biased policing—only that in the aggregate, police are more likely to shoot white people than black people in proportion to their rates of criminal offense. They also don't explain the actual reason why there are racial disparities in crime rates, a phenomenon which may itself be a product of racial discrimination.

Further, the study may be limited by its data sources. While Cesario et al. argue that their use of multiple data sources may obviate this concern, they concede that, "if these data are themselves subject to racial bias, such that Black citizens are overrepresented in these data sets relative to their actual criminal activity, then the denominator in the odds calculations for Black citizens will be artificially high, masking real anti-Black disparity in police shootings."

Lastly, just as comparing rates of shooting to proportions of the population is a methodological choice, so too is the choice to compare rates of shooting to crime rates. As much relies upon an assumption that crime rates predict who police target, and omits other measures of police exposure to citizens. For example, the paper does not capture the way in which police may over-target predominantly minority neighborhoods for policing. The study also does not capture how discretionary stops by police increase individuals' exposure to cops, independent of their crime rates.

Still, the study concludes, the data suggest that we should be cautious about explaining the black-white disparity in police shootings as a function of bias alone.

"We do not discount the role race may play in individual police shootings," Cesario et al. write. "Yet to draw on bias as the sole reason for population-level disparities is unfounded when considering the benchmarks presented here."