# Statistics and Statistical Programming (Winter 2021)/Problem set 7

## Programming Challenges[edit]

**Do police in the United States engage in discriminatory behavior on the basis of race and ethnicity?** For this problem set, you will investigate the relationship between traffic stops, vehicle searches and driver attributes (especially race as recorded by police officers conducting traffic stops). Doing so will involve some more advanced data wrangling, visualization, and analysis. We'll use data from The Stanford Open Policing Project (SOPP) that looks at records of traffic stops in Washington state between January 1, 2009 and September 30, 2018. The full SOPP dataset for Washington is about 11 million rows, so I've created a 1% random sample for us to work with here.

Overall, the dataset is well-documented and pretty "clean" (as far as these things go) but there are still a number of features that may be confusing, weird, and/or ill-organized to help answer the questions I've asked you below. Thank goodness you know how to use R to address these issues...

### PC1. Create a bivariate visualization[edit]

Before we get started with policing data, lets do an "easier" attempt at visualization using `ggplot2`

.

Return the dataset we used in Statistics and Statistical Programming (Winter 2021)/Problem set 5 and load it up the CSV file. You can just find and copy

Visualize two variables in the Problem Set #2 dataset using `ggplot2`

and the `geom_point()`

function to produce a scatterplot of `x`

on the x-axis and `y`

on the y-axis.

**Optional bonus:** Incorporate any of the other variables on other dimensions (e.g., color, shape, and/or size are all good options). If you run into any issues plotting these dimensions, revisit the examples in the tutorial and the ggplot2 documentation and consider that ggplot2 can be very picky about the classes of objects.

### PC2. Learn about the Open Policing data[edit]

Review the project overview on the SOPP homepage, the overview of the data, the description of the standardized data, the codebook/notes for the Washington data from the data_readme.md, as well as any other ancillary materials that you can find that seem likely to help you get oriented with the data.

For the questions below we'll focus on the following measures recorded for each traffic stop in Washington 2009-2018: `date`

, `subject_age`

, `subject_race`

, `subject_sex`

, and `search_conducted`

.

Record any questions or issues you might notice related to these measures as you review the information about the project and dataset.

### PC2. Import, explore, clean[edit]

As I mentioned above, the full WA-SOPP dataset is over 11 million rows, so I have created a random 1% subset for us to work with in this assignment which is our Dropbox here repository here. It's about 28MB.

To get started, you'll want to import the data and explore its structure as well as key variables that we'll be focusing on in this analysis (`date`

, `subject_age`

, `subject_race`

, `subject_sex`

, and `search_conducted`

). Inspect a random sample of rows to get a sense of the data. What (if anything) is missing? You may also want to clean/recode some of the key variables. Make sure to explain and justify any data cleanup and/or recoding steps you decide to take.

### PC3. Summarize outcome and predictor variables[edit]

Calculate and report appropriate summary statistics for the outcome (`search_conducted`

) and each of the predictor variables we care about (`date`

, `subject_age`

, `subject_race`

, and `subject_sex`

). Include visual and/or tabular summaries where appropriate. Attempt, when possible, to write efficient/elegant code that avoids unnecessary repetition while also retaining clarity.

### PC4. Summarize conditional relationships between outcome and predictor variables[edit]

The outcome variable we care about here is a dichotomous indicator for whether each traffic stop resulted in a police search (of either the driver or the vehicle) being conducted. Summarize the relationship between each of the predictor variables (`date`

, `subject_age`

, `subject_race`

, and `subject_sex`

) and the outcome variable (`search_conducted`

). For continuous predictors, be sure to include visual summaries. For categorical predictors, focus on providing cross-tabulations that report conditional summary statistics within groups (for example, compare the numbers of searches conducted across the two categories of `subject_sex`

).

### PC5. Analyze relationships between driver race/ethnicity and vehicle searches over time[edit]

Summarize the relationship between the recorded `subject_race`

for each traffic stop and the `search_conducted`

outcome over the time period covered by the dataset. You may do this in a variety of ways, but a good goal should be to should be to produce the following:

- A plot of the number of stops across the entire sample within each month
- A plot of the number of searches across the entire sample within each month.
- A plot of the number of stops within each
`subject_race`

category each month. - A plot of the number of searches within each
`subject_race`

category each month. - A plot of the proportion all searches accounted for within each
`subject_race`

category each month.

You'll need to build a dataset. My suggestion is draw out the dataset you want to build. What are the rows? What are the columns?

Here's one suggestion for how you might approach this:

1. Create a new data frame that aggregates stop and search data across sub-groups of `subject_race`

per month. This object could include the following columns:

- date as a month/year (should be a date or date-time object which will require a day. I set all of them just to "YYYY-MM-01" by rounding them down)
- race/ethnicity (from the
`subject_race`

variable) - number of stops (within the
`subject_race`

group identified for the row) - number of searches (within the
`subject_race`

group identified for the row) - total number of searches that month/year
- proportion of total searches (within the
`subject_race`

group identified for the row).

*Note that this will result in a data frame with multiple rows per month/year (as many as one row for each subject_race category).*

If your dataset is wide, you will need to turn it into a long dataset for graphing.

2. Use `ggplot2`

and the `geom_line`

layer to generate each of the plots. Note that you'll want to assign `subject_race`

as an aesthetic element (`aes`

) for some of the plots so that ggplot2 represents each category as a separate line (maybe distinguished by color?). Make sure to incorporate useful titles, axis labels, and legends for each plot you produce. Recall that the R tutorials include examples of using `aes`

with `ggplot2`

.

### PC6. Calculate baseline population proportions for relevant race/ethnicity categories[edit]

To help interpret the results of the foregoing analysis of the traffic stop data, we should calculate some baseline population proportions of the same race/ethnicity categories in the state of Washington around the same time that the SOPP data comes from. Luckily, we have access to exactly the data we need to do this via our old friend, the `openintro`

library!

Use the `county_complete`

dataset from the `openintro`

library to calculate the proportions of the Washington population in 2010 in each of the categories identified in the `subject_race`

variable of the traffic stop dataset. You will want to use the codebook for the dataset to identify the variables you'll need. You will also need to wrangle the data a bit to produce the proportions we're looking for. Be sure to note and justify any assumptions and/or recording decisions that you make along the way.

## Statistical Questions[edit]

### SQ1. Interpret the Washington traffic stop analysis (PCs 3-5)[edit]

Return to the questions that motivated this analysis. Based on your results from PCs 3-5, what patterns do you observe in vehicle searches among Washington drivers between 2012-2017? Specifically, what patterns do you note from your comparisons of stops and searches across the categories identified in the `subject_race`

variable? What patterns do you observe when you compare across groups in aggregate (i.e., summed across the entire dataset)? What patterns do you observe in terms of either the numbers or proportions of stops and searches when you compare across groups over time?

### SQ2. Contextualize traffic stop data in relation to population data[edit]

Consider the results of PCs 3-5 in relation to the results of PC 6. Do the results of PC 6 impact your interpretation of PCs 3-5 in any way? How do you relate the results of the traffic stop and vehicle search analysis to the population baseline proportions?

### SQ3. Reflect on the limitations and possible extensions of your analysis[edit]

Identify and briefly explain key limitations of the data, your analysis, and the results in relation to the questions and concepts that motivated the exercise. Where possible, what additional information/data or analysis might you suggest in order to overcome these limitations and answer the questions in a more comprehensive or convincing fashion?