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In which I reach a different conclusion than Tim Wise

February 27, 2010

Tim Wise writes:

Recently, I received an e-mail from a college professor who shows a video of one of my speeches in her classroom. She explained that she was in need of a citation for a claim I had made in the video, to the effect that although blacks and Latinos are far more likely than whites to be searched by police after a traffic stop, it is whites who are more likely–four times more likely in fact–to be found with drugs or other contraband on us, on the much less frequent occasions when we’re the ones searched.

I happily obliged, sending her the web link for a 2005 Department of Justice report, in which the data can be found.

Okay, I admit it. Just like the white male in Tim Wise’s post, I found the above statistic hard to believe. My skepticism was so severe that I clicked the link to the Department of Justice report. Reading it, my skepticism grew when I read that “Other race” drivers were eight times as likely to be found with contraband than black drivers.

My skepticism comes from the magnitude of these differentials. I would, in fact, have guessed that a higher percentage of white drivers were found with contraband. I’ll explain why below. But before getting to the interesting stuff, I’ll quickly show why I was right to be skeptical of “four times more likely.”

A Technical Point

Table 11 of the DoJ report states that 14.5% of searches on white drivers came up with “evidence,” compared to 3.3% of searches on black drivers. But that is actually 3.3%*, because the estimate is based on 10 or fewer cases.

The DoJ surveyed 8,101 black drivers, 1,492 of whom had contact with police (18.4%). 10.2% (152 persons) of them were then searched. 3.3% of those searched were found with “evidence” on their person or in their car. That is, only 5 black respondents were found with “evidence.”

We are working with the Binomial distribution here, so I used a Wilson score interval* to determine that if I wanted a range of numbers that I was 95% certain contained the percentage of searched black drivers who are found with “evidence,” I would say (1.4%, 7.5%).

We can use the normal approximation to find the 95% confidence interval for the percentage of searched white drivers found with “evidence” = (11.1% to 17.9%)

This next step is only defensible if we assume that the errors in our two estimates are uncorrelated. This may be an unrealistic assumption, so take the following with a grain of salt. But if we match our lower bound estimate for whites with our upper bound estimate for blacks, we find that whites are only 1.48 times as likely to be found with evidence. If we match our lower bound estimate for blacks with our upper bound estimate for whites, we find that whites are 12.8 times as likely to be found with evidence.

The uncertainty is even worse for other races: less than 20 “Other race” drivers were searched, so the estimate that 26.5% of those searched were found with “evidence” is absolutely worthless.

The moral: Whites searched at traffic stops are certainly more likely to be found with contraband, but best not to take that “4 times as likely” number too seriously.

A Substantive and Much More Interesting Point

I just showed how much uncertainty there is in that “4 times as likely,” but let’s run with it because it is our most likely estimate. The substantive question, then, is what does 4x tell us? My opinion: that racial profiling is not an efficient law enforcement technique.

Remember that more black drivers (10.2%) are searched than white drivers (3.5%). This tells you that we are not working with a randomly selected sample. Police officers make the decision to search drivers based on that driver’s characteristics. What makes a police officer search a white driver? The driver probably fits a profile: young, male, bloodshot eyes, alcohol on the breath, erratic driving or other behavior. When the officer searches a white driver who fits the law-breaking profile, there is a good chance of finding contraband.

What makes an officer search a black driver? All that other stuff, plus the fact that the driver is black. This additional piece of information makes the officer’s “whom to search” filter less efficient.

Take this logic to the extreme: assume that whites and blacks have identical rates of criminality. Then imagine that I searched every black driver in America, but only white drivers who were unable to drive straight. Close to 0% of black drivers would have contraband in their cars, while close to 100% of white drivers would.

My take: The fact that black drivers are less likely than white drivers to be found with contraband is evidence for how inefficient and widespread racial profiling is not evidence for higher criminality among the white population.

So there’s a good reason to wish for a more precise estimate of that “4 times as likely” statistic. The larger that differential, the more pervasive is racial profiling.


PS – No, I do not think the student described by Wise had the above in mind when he challenged his professor.

Further technical point: Someone could argue that black drivers are searched more often not because they are black, but because of the covariates of being black – on average, blacks are younger and poorer than whites. But the above analysis in effect controls for these covariates. If officers were making decisions based on covariates of race instead of race, then police searches would have the same “success rate” across races, because everyone searched would fit the same profile. But this is clearly not the case.

*Extremely technical point: The normal approximation for the binomial confidence interval was inappropriate for black drivers, because n*p = 5, while the rule of thumb is you need n*p > 5. I just found a very cool Wilson score Confidence Interval calculator, which gave me the following 95% CI: (1.4%, 7.5%).

I did the Standard Error calculation for white drivers by hand:

number with police contact * percentage who were searched: 12199*.035 = 427

Standard error = square root(.145*.855/427) = 0.017


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  1. Is part of the issue here, then, low sub-samples from which to compare?

  2. Right. It’s a great data set: 77,000 respondents and an 82% response rate. But once you slice it up into “Black drivers who were stopped and who were searched” you are already down to 152 people.

    So its definitely fair to say that whites are found with contraband at a higher rate than any other race. But you can’t really put a number to that rate.

  3. Interesting analysis, and BTW, not one with which I disagree, though this may surprise you. My point in making the original argument was never to suggest that whites are more likely to be drug criminals, per se. In fact, I have typically argued a much more sanguine and limited point, based on other data from CDC, etc., namely that drug rates are pretty much equal across racial lines. In some years, white use is higher (and it is always higher among younger persons), but generally it’s equal.

    My argument about the DOJ numbers has always been pretty much yours: that police are making less logical search decisions with black folks, that their standard of suspicion is less precise and their threshhold for suspicion is far lower for blacks than for whites. So they search whites when evidence is stronger, and search blacks for less legit reasons. My reason for bringing it up is to show a) that profiling is happening (which this data and lots of other studies I reference in my books indicate quite clearly), and that b) it is not only racially biased but bad law enforcement. It is also worth noting that even the mere fact of equal drug use rates between whites, blacks and Latinos is counter to most white folks’ beliefs and stereotypes. Most whites (as many as 95% in one focus group) admit that when they hear the term “drug user” they envision a black person. I have done word association exercises with folks in settings, in which they believe they are being monitored for dishonesty and deception (what are known as “bogus pipeline studies”) with similar results. Even folks of color often have internalized these beliefs about their own group(s). So there is substantial value in debunking the notion of greater black and Latino drug use, if for no other reason than to reduce racial bias and the way that bias can unfairly result in the targeting of persons of color by law enforcement.

  4. Hello Tim,

    I am very pleased that you found your way to my post. If my post came across as adversarial, it came from my interest in figuring out where that statistic came from. Your RedRoom post was excellent, and nothing I wrote here takes away from its larger points.

    I completely agree with you on the need to debunk the cultural myth of black and Latino drug use. All of the data I’ve seen on drug use are fairly consistent across data sets: a higher percentage of whites have ever used drugs, but the percentage of each race currently using drugs is almost identical.

    So my only point here was that the DoJ data 1) are unfortunately imprecise, and 2) can’t be used to make inferences about drug use, though it can be used to make inferences about law enforcement techniques. I’m glad to see we agree on this.

    Thank you for commenting here. I really appreciate it.

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