A Quick Review of First Grade Math for Journalists

Here is the most recent example of journalism run amok in the field of mathematics.  The Washington Post ran this headline:

Here are the actual numbers from Chicago for  2009 - 2013:

White drivers found with contraband: 237
Black Drivers found with contraband: 1,232

For those of you that are rusty with your first grade math, 1,232 > 237.

It is true that more black drivers were searched (6,593 versus 906), and that a higher percentage of white drivers that were searched had contraband.  It is also true that the police in many places stop a disproportionate number of black and hispanic drivers, and are much quicker to search them than they are to search white drivers.  But this is not an article about racial profiling.  This is about math, and the headline is a blatant falsehood.  Police found five times as many black drivers with contraband as white drivers.

The article does make one strong point: a higher percentage of white drivers that are searched are caught with contraband.  Again, here are the numbers for 2009 - 2013:

% of white drivers searched and caught with contraband:  26%
% of black drivers searched and caught with contraband:  19%

The article misinterprets this data to make this dubious claim:

The above sentence says that if you randomly stop and search cars, you are more likely to find white drivers with contraband than black drivers with contraband. The statement and the article imply that whites are more likely to be breaking the law than blacks.  There is little evidence to support one race being more or less law abiding than the other, however.  

Here is my reasoning for a more logical (and less racist) explanation:

1. Let's assume that whites and blacks are equally likely to be breaking the law.  

2. Let's assume that there are cops that are quicker to be suspicious of a black driver than a white driver.  (This could be because of the neighborhood the stop is made in, the race of the driver, or other factors.)  Cops are more likely to search a black driver because of this bias.  This leads to searches that are not motivated by real evidence, just a biased hunch. 

3. Let's assume that cops are less suspicious of white drivers, so they need greater evidence to raise suspicion levels to the point that they would search the car.

4. A higher percentage of white drivers are caught with contraband because a higher percentage of their searches were motivated by actual evidence, not a biased hunch.

If the cops want to catch more bad guys, they should pay attention to why they search white drivers, and apply that level of justification across the board.  Then they could catch more bad guys with fewer searches.  Or at least that is what the math seems to say.