Statistics and causal truth: Police edition

As usual, Andrew Sullivan — who has now returned temporarily to blogging, attracted like a moth to the Trump conflagration — manages to take a common, superficially convincing argument, and express it with moral fervour and personal conviction that makes the tenuous logic really conspicuous. In this case, it’s the argument based on the much-discussed study by Roland G. Fryer, Jr. of the rate of various violent outcomes of police stops, finding that black people are more likely than white to be physically abused by police, but not more likely to be shot.

(Here’s an excellent NY Times report, and  the original study.)

…the Black Lives Matter activists, whose core and central argument is that black men are disproportionately killed by cops. The best data shows this is false…  I find [the study] conclusive. Feelings do not, er, trump data in a deliberative democracy. A reader writes:

I understand that there has been the recent study suggesting that given an interaction with a police officer occurs, then the police officer is no more likely to use a gun with a black person than with a white person. However, given that many black men have a much higher rate of interaction with police (such as, anecdotally, Philando Castile, with 52 traffic stops), then is it not fair to say that black men are disproportionately killed by cops?
The point is that there is no evidence of individual racism in these police encounters, despite the impression from many chilling phone videos. The structural bias still exists as a whole, as I said, but the narrative about cops being more likely to kill a black member of the public when encountering him is false.

I have no criticism to make of the study — I have not analysed it in any depth, but it seems credibly and even impressively done — even if I find the premise absurd, that a single study of such a complex phenomenon could be “conclusive”. But they do not “trump” the data that black people make up 13% of the US population, but 31% of those killed during an arrest, and 42% of those killed during an arrest when unarmed. The point is, what these facts (and many others, including the others) mean jointly depends on what we think is the reason for black people being so much more likely to be arrested.

Let’s suppose there are three types of police stops: Low, medium, and high risk. Low risk are interactions with basically harmless people; high-risk are interactions with dangerous, violent individuals, those likely to end in lethal use of force; medium-risk might depend on the skill and intentions of the police officer, whether they are resolved peaceably.

Here are two stories that are perfectly consistent with all the data I have cited:

  1. Black people are more likely than white people to attract the attention of police through dangerous and criminal activity. For this reason they are stopped more frequently than white people. The decision to stop them is not based on racial criteria: While there are more stops of black people, they are distributed among the three categories just like those of white people, hence they are just as likely as white people to lead to lethal violence on the part of the police. Because there is some racism in the interactions, police are more likely to apply non-lethal force to medium-risk black individuals than to whites in the same category.
  2. White and black people commit infractions deserving of police attention with equal frequency, so there are equal rates (by population) of medium- and high-risk police stops involving black and white civilians. Police racism escalates the level of violence applied to low-risk and medium-risk civilians, leading to police killing and injuring black members of the public at much higher levels. This is covered up in the statistics by a very large number of excess police stops of low-risk black individuals, which should contribute very little to the numerator (number of killings), but blows up the denominator (number of stops) to make the rate of killings come out very similar.

We can’t distinguish between these two stories on the basis of these data, and it’s hard to come up with an objective criterion for deciding between them. Story 2 is the basis of the Black Lives Matter narrative, and I find it largely persuasive. There are some data supporting this interpretation, such as this report that stops of black people in NY are half as likely as stops of whites to find weapons, and one-third less likely to find contraband. The fact that Black people are more likely to be shot when unarmed is consistent with this. The Fryer study does consider correcting estimates for “encounter characteristics”, but these are limited, and I think they are based only on the police-reported data which, as we know, are likely to be unreliable precisely when it comes to reporting the nature of an encounter that led to a shooting.

So, as the saying, more research is needed…

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