The voices of Urban Institute's researchers and staff
July 19, 2013

Simpson's Paradox: the logic of racial disparities

July 19, 2013


On Tuesday, we wrote about our analysis of FBI data that describe the circumstances under which fatal shootings are more likely to be considered justified. We described the stark disparity between the rates of justifiable rulings in cases with a white shooter and a black victim compared to those in which the races were reversed. This racial disparity, we argued, is greater than any other in the criminal-justice system and threatens the notion that justice in America is colorblind to its core.

On RealClearPolicy, Robert VerBruggen offers a different perspective. He argues that the racial discrepancy between the rates of justifiable-homicide rulings should not necessarily be taken as evidence of racial bias within the criminal-justice system. Instead, he suggests that these discrepancies may be explained by the differing rates of violent offending between blacks and whites more generally.

His was a compelling piece, and one worth investigating a little further. We have seen this argument in a variety of forms in response to a chart that has been flying around the Internet this week. It is clear why this line of thinking is tempting, but there is a flaw in the logic. This logical flaw, formally known as an ecological fallacy, is common in discussions about racial disparity and often leads to a conclusion that a racial disparity is reasonable when it actually is not.

VerBruggen states that “in a given year, 3.3 of every 1,000 blacks are victimized by white offenders and 3.4 of every 1,000 whites are victimized by black offenders.” He points out that while these victimization rates are nearly identical, actual rates of offending within the population are likely to be very different given that the white population is several times larger than the black population. (In 2010, the population of the United States included 223.5 million white Americans and 38.9 million black Americans.)

Using the victimization rates that VerBruggen provides, we can calculate that there were approximately 737,000 instances of violent victimization of white Americans by black Americans in 2010 and only 128,000 when the races were reversed, a difference of nearly six-fold.

VerBruggen makes an important point about differences in violent offending by race. The conclusion that he draws from this data seems to be that, due to these racially disparate numbers of offenses, you would expect to see higher rates of justifiable rulings in white-on-black crimes compared to black-on-white crimes.

To explore the issue further, suppose we assume that a racially unbiased system would have the same rates of justifiable rulings regardless of race. To see what that would look like, we use the average rate homicides are ruled justifiable from the FBI data -- 2 percent. At the 2 percent FBI rates, we would expect to find that out of 128,000 white on black victimizations reported in the National Crime Victimization Survey (NCVS) data, about 2,500 would be ruled justifiable. And, out of the 767,000 black-on-white victimizations almost 15,000 would be ruled justified. However, if instead we use the actual rates from the FBI data at which white-on-black homicides are ruled to justified (11.41 percent) and black-on-white homicides are adjudicated justfied (1.2 percent), it paints a very different picture: Using these numbers, 14,600 white on black victimizations would be ruled justified, compared to only 8,800 black on white victimizations. Thus, it is clear that racial disparities in homicide rulings remain.

The reason it is so easy to come to the wrong conclusion that the racial disparity is reasonable is what is known as the ecological fallacy, which is mistaking trends in groups for individual behavior. The original example is a half-century-old study that found that immigrants settled in states that studies found to be abnormally illiterate. The implication is that immigrants are more likely to be illiterate. In fact, immigrants were more literate than average; they just settled overwhelmingly into states with higher than average illiteracy rates.

In the case of the racial-disparity data, the ecological fallacy would be inferring that blacks should have a lower rate of justifiable rulings because they are more likely to be the perpetrator. There is no reason to believe from the offending patterns alone that the racial disparities are somehow reasonable.

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I think this misses the point.

The real question is, is it appropriate for you to assume that both groups actually commit justifiable homicides at a rate of 2%.

You're the one applying that population rate to everyone in the population so it seems to me you're the one committing the ecological fallacy, right?

Let's say - as an extreme case - that none of the difference comes from the courts. So 11.4 percent of white-on-black homicides are ACTUALLY justified and 1.2 percent of black-on-white homicides are ACTUALLY justified. The truth is obviously not this stark, it's for the sake of argument.

Even if that were the case there's obviously still work to be done here. Presumably black justifiable homicide is lower because of the conditions that blacks in the U.S. live in - because of other disparities they face. They grow up in bad neighborhoods, get bad educations, face poor job prospects, etc.

It's not ignoring the problem to recognize that the root of the problem might exist somewhere outside the justice system.

In actuality, my prior is that it's a mix - that there is some discrimination in the courts but that a lot of the disparity is real and it's driven by factors outside the criminal justice system (which still need to be rectified! they just need to be rectified differently).

It's been about a decade since my one criminology class, though, so I might be missing something. Is there a reason for you to apply the national justifiable homicide rate to all groups in the population the way you did?

What Daniel said. This analysis entirely misses the real point, which is that race and economic inequality are tightly entwined. If you take the immediate context of the crime into account (as stats usually fail to do), then invariably the disparities in sentencing will seem smaller. An obvious example - there will likely be more black-on-white economically motivated crime than vice versa. This in turn could lead to more 'justified' white on black shootings.

But... if you take the wider context into account (which stats always fail to do), then the different life chances of white and black Americans will tell an entirely different picture. Black-on-white economically motivated crimes reflect the fact that social structures ensure that blacks are poorer than whites, and have quantifiably worse life chances.

Yes the judicial system is racist, but its the socio-economic racism in society at large that is the real problem. You can't understand the former without talking about the latter. A graph or two might grab the attention but its only ever a tiny part of the story. The conclusion might be right, but you're making the wrong argument.

Hey John,

What I'd love to see is a "color blind" investigation into these justifiable homicides. If we consider race as just a proxy for other variables that significantly contribute to one's likelihood of committing a homicide (socioeconomic background, age, etc.), then research into disparities in the outcomes of justifiable homicides for these other variables would seem to be very interesting. Remove race from the dataset and try to find similar trends in what is left.

I would think it clear that no one can doubt there is an imbalance between justifiable homicide outcomes for whites v. blacks but I think the above would be more relevant to policymakers as providing such things as additional school program funding or enhanced policing of certain areas at certain times is easier than changing jurors' racial perceptions.