(a) County-by-county posterior estimates of the risk ratio of being {white, armed, and shot by police} to being {white, unarmed, and shot by police}. Grey bars are county-specific 95% PCI estimates. The blue bar is the nation-wide pooled 95% PCI estimate. The points on the error bars are posterior medians. Data are plotted on the log scale, but are labeled on the natural scale. (b) Map of county-specific posterior median estimates of the risk ratio of being {white, armed, and shot by police} to being {white, unarmed, and shot by police}.

(a) County-by-county posterior estimates of the risk ratio of being {hispanic, armed, and shot by police} to being {hispanic, unarmed, and shot by police}. Grey bars are county-specific 95% PCI estimates. The blue bar is the nation-wide pooled 95% PCI estimate. The points on the error bars are posterior medians. Data are plotted on the log scale, but are labeled on the natural scale. (b) Map of county-specific posterior median estimates of the risk ratio of being {hispanic, armed, and shot by police} to being {hispanic, unarmed, and shot by police}.

(a) County-by-county posterior estimates of the risk ratio of being {black, armed, and shot by police} to being {black, unarmed, and shot by police}. Grey bars are county-specific 95% PCI estimates. The blue bar is the nation-wide pooled 95% PCI estimate. The points on the error bars are posterior medians. Data are plotted on the log scale, but are labeled on the natural scale. (b) Map of county-specific posterior median estimates of the risk ratio of being {black, armed, and shot by police} to being {black, unarmed, and shot by police}.

There is, of course, variation across counties in the U.S. in these risk ratios. Figs 1 , 2 , and 3 plot the posterior distributions of county-specific risk ratios, as well as the geographic distributions of the median estimates.

The median probability across counties of being {black, armed, and shot by police} is 2.79 (PCI95: 1.72, 4.92) times the probability of being {black, unarmed, and shot by police}—the symbol, PCI95, indicates the lower and upper endpoints of central 95% of the posterior density; it is the Bayesian equivalent of a confidence interval. The median probability across counties of being {hispanic, armed, and shot by police} is 3.08 (PCI95: 2.05, 5.10) times the probability of being {hispanic, unarmed, and shot by police}. The median probability across counties of being {white, armed, and shot by police} is 3.33 (PCI95: 2.40, 4.70) times the probability of being {white, unarmed, and shot by police}.

(a) County-by-county posterior estimates of the risk ratio of being {hispanic, armed, and shot by police} to being {white, armed, and shot by police}. Grey bars are county-specific estimates. Grey bars are county-specific 95% PCI estimates. The blue bar is the nation-wide pooled 95% PCI estimate. Data are plotted on the log scale, but are labeled on the natural scale. (b) Map of county-specific posterior median estimates of the risk ratio of being {hispanic, armed, and shot by police} to being {white, armed, and shot by police}.

(a) County-by-county posterior estimates of the risk ratio of being {black, armed, and shot by police} to being {white, armed, and shot by police}. Grey bars are county-specific 95% PCI estimates. The blue bar is the nation-wide pooled 95% PCI estimate. The points on the error bars are posterior medians. Data are plotted on the log scale, but are labeled on the natural scale. (b) Map of county-specific posterior median estimates of the risk ratio of being {black, armed, and shot by police} to being {white, armed, and shot by police}.

As before, there is variation across counties in the U.S. in these relative risk ratios. Figs 4 and 5 plot the county-specific results.

The median probability across counties of being {black, armed, and shot by police} is 2.94 (PCI95: 2.23, 3.86) times the probability of being {white, armed, and shot by police}. The median probability across counties of being {hispanic, armed, and shot by police} is 1.57 (PCI95: 1.14, 2.09) times the probability of being {white, armed, and shot by police}.

(a) County-by-county posterior estimates of the risk ratio of being {hispanic, unarmed, and shot by police} to being {white, unarmed, and shot by police}. Grey bars are county-specific 95% PCI estimates. The blue bar is the nation-wide pooled 95% PCI estimate. The points on the error bars are posterior medians. Data are plotted on the log scale, but are labeled on the natural scale. (b) Map of county-specific posterior median estimates of the risk ratio of being {hispanic, unarmed, and shot by police} to being {white, unarmed, and shot by police}.

(a) County-by-county posterior estimates of the risk ratio of being {black, unarmed, and shot by police} to being {white, unarmed, and shot by police}. Grey bars are county-specific 95% PCI estimates. The blue bar is the nation-wide pooled 95% PCI estimate. The points on the error bars are posterior medians. Data are plotted on the log scale, but are labeled on the natural scale. (b) Map of county-specific posterior median estimates of the risk ratio of being {black, unarmed, and shot by police} to being {white, unarmed, and shot by police}.

As before, there is extensive variation across counties in the U.S. in these relative risk ratios. Figs 6 and 7 plot the posterior distributions of county-specific risk ratios, as well as the geographic distributions of the estimates. It is notable that Miami-Dade (FL, contains Miami), Los Angeles (CA, contains Los Angeles), and Orleans Parish (LA, contains New Orleans), stand out as counties where the ratio of {black, unarmed, and shot by police} to {white, unarmed, and shot by police} is elevated to 22.88 (PCI95: 6.25, 87.70), 10.25 (PCI95: 2.96, 76.05), and 9.29 (PCI95: 1.88, 105.54) respectively. See Data folder of S1 File for additional county-level results; there are several additional counties with highly elevated levels of racial bias in police shootings not listed here.

The median probability across counties of being {black, unarmed, and shot by police} is 3.49 (PCI95: 1.77, 6.04) times the probability of being {white, unarmed, and shot by police}. The median probability across counties of being {hispanic, unarmed, and shot by police} is 1.67 (PCI95: 0.99, 2.68) times the probability of being {white, unarmed, and shot by police}.

(a) County-by-county posterior estimates of the risk ratio of being {hispanic, unarmed, and shot by police} to being {white, armed, and shot by police}. Grey bars are county-specific 95% PCI estimates. The blue bar is the nation-wide pooled 95% PCI estimate. The points on the error bars are posterior medians. Data are plotted on the log scale, but are labeled on the natural scale. (b) Map of county-specific posterior median estimates of the risk ratio of being {hispanic, armed, and shot by police} to being {white, unarmed, and shot by police}.

(a) County-by-county posterior estimates of the risk ratio of being {black, unarmed, and shot by police} to being {white, armed, and shot by police}. Grey bars are county-specific 95% PCI estimates. The blue bar is the nation-wide pooled 95% PCI estimate. The points on the error bars are posterior medians. Data are plotted on the log scale, but are labeled on the natural scale. (b) Map of county-specific posterior median estimates of the risk ratio of being {black, unarmed, and shot by police} to being {white, armed, and shot by police}.

Figs 8 and 9 plot the posterior distributions of county-specific risk ratios, as well as the geographic distributions of the estimates. It is notable that Miami-Dade (FL, contains Miami), Harris (TX, contains Houston), and Cook (IL, contains Chicago), stand out as counties where the ratio of {black, unarmed, and shot by police} to {white, armed, and shot by police} is elevated to 19.08 (PCI95: 4.46, 81.13), 6.71 (PCI95: 1.46, 26.77), and 5.60 (PCI95: 1.25, 21.97) respectively. As before, the Data folder of S1 File shows that there are several other counties with highly elevated relative risk ratios in addition to those discussed above.

It is worth noting, that on average across counties in the United States, an individual is as likely to be {black, unarmed, and shot by police} as {white, armed, and shot by police}, with a median relative risk estimate of 1.04 (PCI95: 0.62, 1.61). The corresponding ratio for hispanics is 0.52 (PCI95: 0.32, 0.75).

5. County-Level Racial Bias in Police Shootings as a Function of County-Level Properties

Understanding the source of racial bias in police shootings is difficult to do from county-level data, as the ecological inference fallacy can potentially obscure any results [39]. County-level data are far too coarse to use to reliably tease apart the conditions that drive racial bias in police shootings; more reliable findings will likely be based on rigorous, yet qualitative, investigations that are resolved to a more local level. Nevertheless, previous quantitative studies have used regression models on county-level data to compare theories about the county-level correlates of racial bias in police homicide [15, 35–38]. For comparability, this study uses similar models to analyze the USPSD data, contrasting the predictions from conflict and community violence theories, and testing a hypothesis about the possible association of community-level norms about racism and racial bias in police shooting.

Figs 10, 11, 12, 13, and 14 present the geographic distributions of the predictor variables used in the analysis; the outcome variables are: 1) the risk ratio of {black, unarmed, and shot by police} to {white, unarmed, and shot by police}, and 2) the risk ratio of {black, unarmed, and shot by police} to {white, armed, and shot by police}.

PPT PowerPoint slide

PowerPoint slide PNG larger image

larger image TIFF original image Download: Fig 10. Data on Race-Specific Assault-Related Arrest Rates. In these figures, only counties with greater than one arrest are plotted. (a) County-specific Department of Justice data on assault-related arrests (White), per 10,000 residents (2012). (b) County-specific Department of Justice data on assault-related arrests (Black), per 10,000 residents (2012). https://doi.org/10.1371/journal.pone.0141854.g010

PPT PowerPoint slide

PowerPoint slide PNG larger image

larger image TIFF original image Download: Fig 11. Data on Race-Specific Weapons-Related Arrest Rates. In these figures, only counties with greater than one arrest are plotted. (a) County-specific Department of Justice data on weapons-related arrests (White), per 10,000 residents (2012). (b) County-specific Department of Justice data on weapons-related arrests (Black), per 10,000 residents (2012). https://doi.org/10.1371/journal.pone.0141854.g011

Table 1 presents the results of modeling the risk ratio of {black, unarmed, and shot by police} to {white, unarmed, and shot by police}. Across models, there are some consistent trends: 1) population size is positively and reliably associated with the outcome, as is 2) the ratio of the black population size to the white population size; 3) median income shows a reliable negative association with the outcome; 4) the Gini index shows a reliable positive relationship with the outcome; 5) there is a consistently positive, though imprecisely estimated, relationship between the Google search data proxy of local-level racist norms and racial bias in police shooting; and, 6) there is no consistent relationship between the race-specific crime proxies (neither assault-related nor weapons-related arrest rates) and racial bias in police shootings.

PPT PowerPoint slide

PowerPoint slide PNG larger image

larger image TIFF original image Download: Table 1. Predictors of an increased county-level risk of being {black, unarmed, and shot by police} relative to being {white, unarmed, and shot by police}. Values are: posterior mean (posterior standard deviation) of the regression coefficients. The symbol log referes to the natural logarithm. Pop refers to absolute population size. Pct. B. refers to the percentage of the county population that is black. Md. In. refers to median income. Gini refers to the Gini index of inequality. GRP refers to the Google search racism proxy. W. Ast and B. Ast refer to the white- and black-specific arrest rates for assualt, respectively. W. Wps and B. Wps refer to the white- and black-specific arrest rates for weapons violations, respectively. Posterior probabilty that a postive regression coeffcient is less than zero (or a negative one greater than zero) is coded as: * indicates a probability between 0.10 and 0.05, ** indicates a probability between 0.05 and 0.01, and *** indicates a probability of 0.01 or less. https://doi.org/10.1371/journal.pone.0141854.t001

Table 2 presents the results of modeling the risk ratio of {black, unarmed, and shot by police} to {white, armed, and shot by police}. In this case, there are much more reliable positive effects for: 1) population size, and 2) the ratio of black population size to the white population size. As before, 3) median income shows a negative association with the outcome, and 4) the Gini index shows a positive relationship with the outcome; 5) there is a consistently positive, though imprecisely estimated, relationship between the Google search data proxy of local-level racist norms and racial bias in police shooting; and, 6) there is no consistent relationship between the race-specific crime proxies (neither assault-related nor weapons-related arrest rates) and racial bias in police shootings.

PPT PowerPoint slide

PowerPoint slide PNG larger image

larger image TIFF original image Download: Table 2. Predictors of an increased county-level risk of being {black, unarmed, and shot by police} relative to being {white, armed, and shot by police}. Values are: posterior mean (posterior standard deviation) of the regression coefficients. The symbol log referes to the natural logarithm. Pop refers to absolute population size. Pct. B. refers to the percentage of the county population that is black. Md. In. refers to median income. Gini refers to the Gini index of inequality. GRP refers to the Google search racism proxy. W. Ast and B. Ast refer to the white- and black-specific arrest rates for assualt, respectively. W. Wps and B. Wps refer to the white- and black-specific arrest rates for weapons violations, respectively. Posterior probabilty that a postive regression coeffcient is less than zero (or a negative one greater than zero) is coded as: * indicates a probability between 0.10 and 0.05, ** indicates a probability between 0.05 and 0.01, and *** indicates a probability of 0.01 or less. https://doi.org/10.1371/journal.pone.0141854.t002

In effect, larger county population size, a higher proportion of black residents in the population, lower median income, and greater disparities in income all appear to be reliably associated with an elevated ratio of police shooting rate against unarmed black individuals relative to unarmed—and even armed—whites.

In each model that considers them, race-specific crime rates are always entered as simultaneous predictors (see Tables 1 and 2). This model parameterization allows us to examine the effects of race-specific crime rates on racial bias in police shootings. However, there are questions that this model parameterization precludes. Most importantly, having an aggregated measure of crime rate would allow one to test the questions: 1) does racial bias in police shooting increase in areas where crime is generally more prevalent? And, 2) as the difference of black crime rate minus white crime rate increases, does racial bias in police shootings also increase?

As a robustness check, the results from two alternative model parameterizations in predicting the relative risk of being {unarmed, black, and shot by police} to being {unarmed, white, and shot by police} are presented. These models are based on including the sum and difference of race-specific crime rates in the regression; see Appendix.pdf in S1 File. The results of these supplementary models are qualitatively the same as those of the main models; racial bias in police shooting is not reliably associated with crime rate and not related to the difference in race-specific crime rates.