Problem Set 6: Sampling from a Voter File

This problem set is due on November 8, 2023 at 11:59pm.

You can find instructions for obtaining and submitting problem sets here.

You can find the GitHub Classroom link to download the template repository on the Ed Board

Background

In this exercise, we will focus on sampling and sampling distributions when we have access to an entire census for a given population. In this case, the data/durham.csv file contains anonymized data on all registered voters in Durham County, NC that were registered to vote on election day of the 2020 presidential election. The variables in this dataset are:

Name	Description
`ncid`	unique voter identification number
`reg_year`	did person vote (1) or not (0) in 1994?
`age`	age of registered voter
`gender`	voter gender identity (`"F"` = Female, `"M"` = Male, `"U"` = Undeclared)
`race`	voter racial identity (see table below)
`latino`	voter identifies as Hispanic or Latino (`"HL"`), does not (`"NL"`), or undesignated (`"UN"`)
`party`	party registration (`"DEM"` = Democrat, `"Rep"` = Republican, `"LIB"` = Libertarian, `"GRE"` = Green, `"UNA"` = Unaffiliated)
`drivers_lic`	voter has drivers license (1) or not (0)?

North Carolina provides the voter history data in a separate file with a row for each voter who actually casts a ballot in a given election. In the data/vote_history.csv file is a row for every voter that cast a ballot in the 2020 general election. The variables in this dataset are:

Name	Description
`ncid`	unique voter identification number
`vote_method_2020`	method of voting in 2020 general election

For the purposed of this exercise, we will treat the voter list from durhman.csv as the population of interest. Doing so is an increasingly common approach for polling, where pollsters are now using the voter file as a sampling frame to conduct their polls. We will repeated sample from this population to better understand sampling uncertainty.

Note: please follow the directions carefully about setting the seed for the sampling based questions.

In the Durham data, the racial category codes are:

Race	Description
A	ASIAN
B	BLACK or AFRICAN AMERICAN
I	AMERICAN INDIAN or ALASKA NATIVE
M	TWO or MORE RACES
O	OTHER
P	NATIVE HAWAIIAN or PACIFIC ISLANDER
U	UNDESIGNATED
W	WHITE

Question 1 (6 points)

Load the voter list data (data/durham.csv) into R using read_csv and save the data as durham and use the same function to load in the voter history data (data/vote_history.csv) as vote_history. Use left_join to merge the voter history data into the voter list data so that all rows of the voter list remain. Use the ncid variable to join the data sets and save this merged data as durham.

Any registered voter who did not turn out in the 2020 general election will not appear in the vote_history data so their vote_method_2020 variable will be missing in the merged data. Create a new variable called vote_gen_2020 that is 1 if the voter turned out and 0 otherwise (the is.na() function may be helpful).

In the write-up, state how many units are in the population (that is, how many rows are in the durham data) and the proportion of registered voters that actually voted in the 2020 elections.

Rubric: 1pt for Rmd file compiling (autograder); 3pt for data loaded and merged (autograder), 1pt for creation of the vote_gen_2020 variable (autograder); 1pt for number of rows and turnout proportion reported (PDF).

Question 2 (4 points)

Create a density histogram of age with a bin width of 1 and save this plot as age_hist (use the aesthetic mapping y = after_stat(density) in to accomplish this). Create a barplot for turnout (vote_gen_2020) with the proportion on the y-axis (use the aesthetic mapping y = after_stat(prop) in geom_barplot to achieve this). For a slightly nicer plot, use the width = 1 argument. Make sure both of these plots are shown in the PDF.

Rubric: 2pts for age_hist (autograder); 2pts for turnout_hist (autograder).

Question 3 (5 points)

Use summarize() to calculate the population mean and standard deviation of age and vote_gen_2020 (that is the mean and SD of these variables in the durham data) and save the resulting tibble as pop_parameters with the tibble output looking like:

# A tibble: 1 × 4
  age_pop_mean age_pop_sd turnout_pop_prop turnout_pop_sd
         <dbl>      <dbl>            <dbl>          <dbl>
1         XX.X       XX.X            X.XXX          X.XXX

Make sure that the column names are the same for the autograder. (Hint: you can summarize multiple variables in the same call to summarize.) Use knitr::kable() to present the values in nicely formatted table with digits = 2 to create nicely rounded numbers and informative column names (they may need to be abbreviated to fit on the page).

Rubric: 4pts for correct pop_parameters tibble (autograder); 1pts for nicely formatted table (PDF).

Question 4 (8 points)

In the first line of the code chunk for this question use the following code:

library(infer)
set.seed(02138)

Then use rep_slice_sample() to take 1,000 samples of size 200 from durham and calculate the sample mean of age and the sample mean/proportion of turnout for each of these samples. Save these as variables named age_mean and turnout_prop and save the resulting tibble as samples_n200.

Create a density histogram of the age means and save this as age_mean_hist (use a bin width of 0.5). Create a density histogram of the turnout proportions and save this as turnout_prop_hist (use a bin width of 0.005) (NOTE: this is not a bar plot like in Question 2). Make sure both of these plots are shown in the PDF and that they have informative labels.

In the write-up, compare the sampling distribution of the sample mean and sample proportion here to the population distributions from question 2. Are the shapes of the sampling distributions similar or different to the population distributions? If different, how are they different?

Rubric: 2pts for correct sample_n200 output (autograder); 2pts for correct age_mean_hist (autograder); 2pts for correct turnout_prop_hist (autograder); 1pt informative labels (PDF); 1pt comparison to population distributions (PDF).

Question 5 (7 points)

Use the summarize() function on samples_n200 to calculate the average (named ev_age and ev_turnout) and standard deviation (named se_age and se_turnout) of each sample mean/proportion across the repeated samples. Save this tibble as samp_dist_summary and it should look like this:

# A tibble: 1 × 4
  ev_age se_age ev_turnout se_turnout
   <dbl>  <dbl>      <dbl>      <dbl>
1   X.XX   X.XX      X.XXX      X.XXX

Make sure that the column names are the same for the autograder. Use knitr::kable() to present the values in nicely formatted table with digits = 2 to create nicely rounded numbers.

Compare the mean and SD of these sampling distributions to the population means and SDs from the previous question. Are these distributions centered on the same value? Which has more spread, the population distribution of age/turnout or the sampling distributions of their means?

Rubric: 4pts for correct samp_dist_summary tibble (autograder); 1pt for nicely formatted table (PDF); 2pts for discussion (PDF).

Question 6 (5 points)

Now suppose we received a bad voter file that only contained voters under the age of 30 at the time of the 2020 election. Set the seed using set.seed(02138) and repeat the replicate sampling from Question 3 to take 1,000 samples of size 200 from durham after removing voters 30 and over. Calculate the sample proportion of turnout for each of these samples. Save this as a variable named turnout_prop and save the resulting tibble as young_samples_n200.

Create a density histogram of the turnout proportions with informative labels and add a vertical line at the true population average turnout (of all ages). Save this plot as young_turnout_prop_hist.

Does the sampling distribution of turnout in these samples appear biased or unbiased for the population average turnout? Explain why based on the sampling process.

Rubric: 2pts for correct young_samples_n200 tibble (autograder); 1pt for correctly identifying biased/unbiased (PDF); 2pt explaining bias/unbiasedness (PDF).