The Washington Post has been tracking police killings across the nation. Last week, Peter Aldhous published an analysis of these data.1 He figured that blacks suspects were 37.8% of all unarmed suspects killed by police. White suspects made up a nearly similar percentage of unarmed suspects killed by police, despite the fact that there are almost five times as many whites in the United States as blacks.
This does not provide the best evidence to adjudicate racial disparities in police violence, however. Aldous writes:
Video of McDonald’s last moments, shot 16 times by a white officer, made a stark contrast with images of a handcuffed Robert Lewis Dear, the white suspect in the shooting at a Planned Parenthood clinic in Colorado Springs — as activists were quick to point out.
Rather than figure out the probability that an unarmed suspect was black, it would be important to know the probability that a black suspect
shotkilled by police was unarmed. We care less whether an unarmed victim was black as we do whether a black victim was unarmed. That would be more in line with, though not exactly equivalent to, what Aldhous wrote.2
Below, I try to explain how we can use rules of probability to explain this problem to an introductory statistics class.
In my statistics class, I teach students that probability equals the number of events that we care about divided the total number of events for which that event is possible. Let’s start by figuring out the probability that the police
shootkill an unarmed black man. The numerator — the events we care about — would be the number of unarmed black men shot. The denominator — the total number of events — equals all police shootings that kill a suspect, which comprises 867 police shootings.
The numerator is a little trickier. Since we want to know how many unarmed black men are
shotkilled, our best estimate absent any additional data would be the overall probability that a suspect killed by the police was unarmed. This prior probability equals 9.46% since 82 of 867 suspects in the data were unarmed. But, fortunately, we have more data — we know the probability that an unarmed person was black. The data comprised 82 unarmed suspects, of whom 31 were black. The likelihood, therefore, that an unarmed suspect was black is 37.8%, which is the probability that Aldhous calculated. This represents the rate at which unarmed suspects killed by police are black.
We finish calculating the numerator by multiplying these two values together. We multiply the probability of a suspect being unarmed by the rate at which unarmed victims are black, 9.46% (or 82 of 867) by 37.8% (31 of 82). The result of that multiplication represents the probability that a suspect was both black and unarmed, which was 31 out of 867 cases or 3.58%. If you hear about a police shooting that killed the suspect, about one out of every 28 times the police have shot an unarmed black person.
That does not sound too bad, but remember that almost 4% of all
shootingspolice killings are of unarmed black men. We change the denominator from being all possible events — in this case 867 police shootings — to include only those that involve black men. In other words, we divide the 3.58% of all shootings by the probability that a police shooting involved a black suspect. Of the 867 shootings, 235 involved black suspects, making the probability of police killing a black 27.1%.
Dividing 3.58% by 27.1%, we find that about 13% of black men
shotkilled by police are unarmed. This means that if you hear that the police shot a black person, you can guess that about one out of every eight times the suspect would be unarmed.
That provides a discouraging picture of what it means to be black and be policed by in America. But police work is difficult and not every unarmed suspect should be considered safe to officers or the public. It could well be true that the unarmed suspect posed an imminent danger to public safety.
If that is the case, however, then we would expect unarmed white suspects to be killed at a similar rate to blacks. Using the same statistical principles that I did above, which mathematicians call Bayes’ Theorem, we can figure out the analogous rate for whites. When we do, I calculate that unarmed white victims make up 29 of the 867, or 3.34%, of all shootings, while 443, or 51.1%, of the
shootingspolice killings involved whites. This results in a probability that a white suspect killed by police was unarmed, or about one in every 16 shootings of white suspects.
These calculations mean that
the police are twice as likely to have killed an unarmed suspect if that suspect is black rather than white.a black suspect killed by the police is twice as likely to be unarmed as a white suspect to be killed by the police. I don’t know that I have much else that I can add — the number, in this case, kind of does speak for itself.
The data that I use here are those posted by Aldhous and are, thus, out of date with the most current Washington Post analysis of officer-involved shooting deaths, which sadly continues to increase rapidly.â†©
UPDATE As Andrew Wheeler pointed out, I used "shot" and "killed" interchangeably, which is incorrect. The dataset only includes suspects who have been killed by the police. I should have been more careful in the language that I used. I have edited the post to be consistent with the probability that I solved. I regret the error.â†©
UPDATE 2: This will teach me to try to post while my mind is fried grading. One more edit for correction to get the conditional correct in the last paragraph.