September 20, 2021

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Examining the Math and Ethics of Covid-19 in Prisons

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Students in U.S. high schools can get free digital access to The New York Times until Sept. 1, 2021.

Featured Article: “Incarcerated and Infected: How the Virus Tore Through the U.S. Prison System

Prisons were not built to handle pandemics. In fact, it’s hard to imagine worse conditions for preventing the spread of the coronavirus than those in prisons: large groups of people living together, in crowded indoor spaces, with a security staff that comes and goes regularly.

A recent New York Times report found that the rate of Covid-19 cases in United States correctional institutions was more than three times the rate in the general population. A follow-up report found that the infection rate in detention centers run by Immigration and Customs Enforcement (ICE) was 20 times that of the general population.

This data raises important questions, both statistical and moral. In this lesson, you will analyze the pandemic’s impact on correctional facilities across the United States — and close to home. Then you will have the opportunity to weigh the ethics of prioritizing — or not prioritizing — prison communities for vaccination, and to explore the realities of statistical bias in data collection.

Look closely at the graph below. These connected-dot plots compare the coronavirus infection rates in each state’s entire population with the rates in its state prisons, including for incarcerated people and prison staff.

Read the beginning of the article (until you reach the graph above), then answer the following questions:

1. The graph in the warm-up activity reveals the disproportionately high Covid rates in state prisons across the United States compared with the general population. Why are correctional facilities “among the nation’s most dangerous places when it comes to infections from the coronavirus”?

2. How did The New York Times collect this data?

3. After reading this introductory section, what are your reactions to what you learned about Covid in prisons? Why?

Note to teachers: Answers to the math problems are at the bottom of this post. Classes can do the activity below with any county that has a state or federal correctional facility on the map in the article. They will explore their home county in Math Activity #2.

According to the map “Inmate infections in U.S. correctional facilities,” in the featured article, San Quentin State Prison has had 2,243 Covid-19 cases and 28 Covid-related deaths during the pandemic. The peak number of prisoners over that time was 3,462. The prison is in Marin County, Calif., which has had 13,855 Covid-19 cases and 227 deaths in its general population. According to the Census Bureau, Marin County has 258,826 residents. The following table summarizes this information:

Imagine that a local politician says, “There have been more than six times as many Covid-19 cases in our county than in the prison. In addition, there have been more than eight times as many deaths. So, let’s focus on disease mitigation among the county’s citizens, who clearly have been more affected than people in prison.”

Are the numbers in the politician’s statement accurate? How might they be misleading?

1. Verify the politician’s statistics by showing:

2. Answer the following, in writing or in class discussion:

3. One way to measure the impact of Covid-19 is by calculating infection and death rates. Two formulas for these statistics are given below:

4. Answer the following, in writing or in class discussion:

Let’s find, calculate and interpret measures of Covid-19’s spread in your community and in nearby prison facilities. Draw a blank table, similar to the one we used in the warm-up:

First, find the closest prison to your community using the interactive map in the article. Hover your cursor over the circle representing the prison, and then fill in the cells in the table under the “nearby prison” column. (Use the “inmates at peak” statistic as the population size.)

Next, open the New York Times Covid-19 database. Navigate to the “County trends” section and find your county. Change the menu from “Recent trends” to “All time.” Fill in the corresponding cells in the table with the case count and the death count. To find your county’s population size, look up your county name in the U.S. Census Bureau’s Quick Facts site.

Once you’ve compiled all the data, respond to the following:

  • Calculate and compare the infection rates in your county with those in the nearby prison. Which one is higher? Why do you think that is?

  • Calculate and compare the death rates in your county with those in the nearby prison. Which one is higher? Why do you think that is?

Option 1: Weigh the ethics of prioritizing prison communities for vaccination.

Before Covid vaccines were widely available in the United States, the Centers for Disease Control and Prevention recommended that prison workers and incarcerated people be placed in early phases of the rollout. Responses were mixed. Read the following two quotes from a March article about how Covid-19 prison vaccination policies differed from state to state:

“There’s no way [the vaccine is] going to go to prisoners before it goes to people who haven’t committed any crime.” — Jared Polis, Governor of Colorado

“People are unwilling to say we should vaccinate people who are incarcerated — who may have done something bad — before us. It’s like, ‘How dare they?’ But that’s not the question here. It’s not what we value or who we value. This is about who is at risk of disease. That’s it.” — Dr. Jaimie Meyer, associate professor at the Yale School of Medicine

The Advisory Committee on Immunization Practices, a panel of independent experts who advise the C.D.C. on its vaccine policies, identified four ethical principles to guide their decision-making process when vaccine supply is limited:

  • Maximize benefits and minimize harms — Respect and care for people using the best available data to promote public health and minimize death and severe illness.

  • Mitigate health inequities — Reduce health disparities in the burden of Covid-19 disease and death, and make sure everyone has the opportunity to be as healthy as possible.

  • Promote justice — Treat affected groups, populations and communities fairly. Remove unfair, unjust and avoidable barriers to Covid-19 vaccination.

  • Promote transparency — Make a decision that is clear, understandable and open for review. Allow and seek public participation in the creation and review of the decision processes.

Imagine that you are the governor of your state. Use those four principles to help guide your vaccine prioritization plan and determine what priority status prisoners and prison workers should have as part of the vaccine rollout. What recommendations would you make?

Option 2: Explore the potential for statistical bias.

Let’s dig a bit deeper into how these statistics were generated. Reread this paragraph from the article:

The cramped, often unsanitary settings of correctional institutions have been ideal for incubating and transmitting disease. Social distancing is not an option. Testing was not a priority inside prisons early in the pandemic. With little public pressure, political leaders have been slow to confront the spread.

Statistical bias occurs when a method for estimating a quantity, such as using case counts to estimate the total number of infections in a prison, is inaccurate. Biased methods lead to overestimates or underestimates.

  • Given that testing for the coronavirus was “not a priority inside prisons early in the pandemic,” do you think the prison infection rates listed in the article are biased? If so, are they underestimates or overestimates?

Now, let’s think about estimating the infection rate outside of prisons.

  • Think about the testing conditions in your community during the pandemic. Do you think there are people who were infected with Covid-19 who never got tested? Why? Do you believe the overall infection rates listed in the article are biased? If so, are they underestimates or overestimates?

  • In your opinion, how should we deal with the possibility of statistical bias in the data we analyzed? How much should statistical bias affect our conclusions?

This lesson was written by Dashiell Young-Saver, who is a high school teacher of statistics and the founder of the site Skew the Script. Sharon Hessney, who curates the Learning Network’s weekly feature “What’s Going On in This Graph?” contributed to the lesson.

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