Math for the People

Subsection 7.7.1 Are stopped drivers searched more often if they are Black?

Once a driver is stopped, officers may or may not search them or their vehicle. We can use the table function we've used before in a new way to help us analyze if a driver's race is related to whether or not they are searched.

In Hartford, we already saw that there were 3589 stops of Black drivers. In our new table, we see that 925 of these drivers were searched in some way (look at the TRUE row and black column). The remaining 2664 were not searched. For white drivers, 835 were searched out of a total of 3486 who were stopped. Therefore,

of stopped Black drivers were searched while

of stopped white drivers were searched. Stopped Black drivers seem to be searched at slightly higher rate than stopped white drivers. But perhaps the Black drivers have contraband at a slightly higher rate as well?

We use the table function again, but this time include whether or not contraband was found.

The resulting table is a little more complicated--in fact, you probably see two tables! In the first table, all the entries are 0. The reason for these zeros is that we first consider all drivers who were not searched or frisked. There is no way to find contraband in this case, so the entry in the contraband column is NA--neither TRUE nor FALSE--so all of the entries are 0.

The second table includes all of the drivers who were searched or frisked. Notice that contraband was found for 8 of the 925 searched or frisked Black drivers, or \(0.9\%\text{,}\) and for 10 of the 835 searched or frisked white drivers, or \(1.2\%\text{.}\) We see that the proportion of white drivers who were stopped or frisked and who possess contraband is slightly higher than that for Black drivers. It is therefore possible that officers are searching Black drivers on less evidence than they are for white drivers.

In summary, in Hartford between April 2014 and September 2016, it seems as though Black drivers were not stopped disproportionately. Stopped Black drivers were searched or frisked at a slightly higher rate than stopped white drivers, and contraband was found on a slightly higher percentage of searched or frisked white drivers than searched or frisked Black drivers. While we cannot make any definitive conclusions based on our analysis, it seems as though there was a small anti-Black bias in vehicular stops and searches, but there did not seem to be large-scale, widespread racial disparities. You should edit the blocks of code above and see what conclusions you can make for the Philadelphia data.

Subsection 7.7.2 Applying Bayes' Theorem to policing: practice problem

Bayes theorem also gives us a tidy way to analyze probabilities in police interactions. Consider the following scenario: the residents of Fourtown have recently been complaining of age discrimination. They would like to calculate the probability of being searched given that the motorist was over 65.

We know that of the 100 police stops in the last year, 50 ended in searches. Of those 100 stops, 80 were over the age of 65. Thirty of those motorists over 65 years of age were searched. What is the probability of a Fourtown motorist being searched, given that they are over the age of 65?

We can use Bayes' Theorem! If \(A\) is the event that a motorist is searched and \(B\) is the event that a motorist is 65 years old or older, we see that

Subsection 7.7.3 Using Google Colab and Python to analyze a large police stop dataset

To analyze a large police stop dataset, we'll need some more advanced tools. Use this Google Colab notebook to look deeper into the data on police stops and racism.¹

Make a copy of the notebook by going to File \(\rightarrow\) Save a copy in Drive, then navigate to your Google Drive and follow along through the notebook.