# 12 DSJ Investigation: Police Interactions

DSJ INVESTIGATION: Police Interactions in Oakland, CA

MATH SKILL FOCUS: Using Contingency Tables to Calculate Probabilities

In April of 2014, 682 black people were stopped by police and 299 white people were stopped by police. According to the census for the City of Oakland in California, in the 2010’s, the population was:

- White population: about 135,000 people (34.5% of the total population)
- Black population: about 110,000 people (28% of the total population)

Make a contingency table reflecting this, then answer the questions that follow.

Black | White | Total | |

Stopped by Police | |||

Not Stopped by Police | |||

Total |

- What is the probability of an Oakland city citizen being stopped by the police?
- What is the probability that a person is stopped by police, given that they are black?
- What is the probability that a person is stopped by police, given that they are white?
- If you see a person who is stopped by the police, what is the probability that person is black?

Researchers from Stanford University conducted a study on the Oakland Police Department, looking for racial bias in how the police interacted with people. The researchers looked at videos from body cameras the police were wearing as well as the data from police records. The following data came from the 981 times police stopped drivers in Oakland in April 2014.

Black | White | Total | |

Searched | 113 | 2 | |

Not Searched | 569 | 297 | |

Total |

Complete the contingency table above, then answer the questions that follow.

- What is the probability that someone stopped by the police was searched?
- What is the probability that a person was searched, given that they are black?
- What is the probability that a person was searched, given that they are white?
- If you see a search in progress, what is the probability that the suspect is black?

Create an EXPECTED frequency table for behavior at police stops if there were no evidence of racial bias. Use the same 981 people that were stopped in the last scenario. If police were fair in who they searched or didn’t search, the percentage for black and white people searched should be the same (an unbiased response would be the percentage answer you found to question 1 in the last problem). Use this percentage to change the “Black Searched”, “White Searched”, “Black Not Searched” and “White Not Searched” values so they do not reflect racial bias.

Black | White | Total | |

Searched | |||

Not Searched | |||

Total | 682 | 299 | 981 |

After determining if the person at a stop was searched, the Stanford study also recorded what happened at the end of each of the 981 police stop interactions. Use the following information to fill in the table. Note that the number of black and white people stopped are the same as in the previous study.

- A total of 41 people were arrested.
- There were 369 black people that received a citation.
- A total of 386 people received a warning. Of those 113 were white.

Black | White | Total | |

Arrest | |||

Citation/Ticket | |||

Warning | |||

Total | 682 | 299 | 981 |

- What is the probability that someone stopped by the police was arrested?
- What is the probability that a person was arrested, given that they are black?
- What is the probability that a person was arrested, given that they are white?
- If you see an arrest in progress, what is the probability that the suspect is black?
- What is the probability that someone stopped by the police was given a citation?
- What is the probability that a person was given a citation, given that they are black?
- What is the probability that a person was given a citation, given that they are white?
- If you see a citation being written, what is the probability that the suspect is black?
- What is the probability that someone stopped by the police was only given a warning?
- What is the probability that a person was given a warning, given that they are black?
- What is the probability that a person was given a warning, given that they are white?
- If a person got away with only a warning, what is the probability that the suspect was white?

Black | White | Total | |

Arrest | |||

Citation/Ticket | |||

Warning | |||

Total | 682 | 299 | 981 |

Do you think this shows evidence of police bias within the Oakland city police department at the time? Why or why not? What other information might you need to better answer this question?