Chapter 5

Racial Bias in Jury Selection

Introduction | The Binomial Model | References and Resources


The Supreme Court We are all biased in some way. Humans will inevitably evaluate new things based on their past experience and knowledge, and these biases can effect us in systematic ways. In this project, we will examine the possibility of racial bias in jury selection by looking at two actual court cases tried in the United States.

In each case, an African-American was on trial and each had a jury with no African-Americans seated. We will first examine a case study of the Swain trial, and consider questions raised during that case. Next, we will consider a different set of data based on a more recent trial in Monroe County, Alabama, which has a population of 24,000. The proportion of whites in that county is 58%; the proportion of blacks is 40%. In each of these cases, the possibility of racial bias in the selection of the juries was raised on their appeal. In each case, the higher court determined that there was insufficient evidence of racial bias. Each defendant was convicted and given the death sentence.

If the proportion of African-Americans in a community is 40%, what is the chance of randomly selecting 12 people from the community and obtaining a sample with zero African-Americans? This question is a gross oversimplification of the facts underlying the cases, but it is a part of the evidence that was considered in the aftermath of both convictions. 

1. Read the summary of the Swain Case from the UCLA Department of Statistics.

2. Read the summary of the Horsley Case from the Institute for Global Communications.

The first three paragraphs of this transcript of Horsley's appeal provide a good overview of the facts surrounding Horsley's crimes. As you can see, there is little doubt of Horsley's guilt and many issues were raised in consideration of his sentencing.

3. Read the fifth footnote of Horsley v. Alabama, United States Court of Appeals. Note in particular that the Swain case was raised in Horsley's trial. 

4. Read the article Sociologist testifies about how to overcome racial bias in jury selection by Jennifer McNulty


The Binomial Model

Racial bias in jury selection is a complex situation; this project oversimplifies the issue so we can explore it with the statistical tools in this chapter. However, it is important to remember that statistics is only one tool among many. Several types of information are needed to determine the truth behind the issue of racial discrimination.

Suppose that 12 people are chosen at random for a jury from a large population in which 40% are black and 60% white.

6. Argue that the number of black persons chosen for the jury has (at least approximately) the binomial distribution with parameters n = 12 and p = 0.4.

Hence, the probability that there are x black persons on the jury is

f(x) = C(12, x) 0.4x 0.612 - x for x = 0, 1, ..., 12,

where C(12, x) is the binomial coefficient 12! / [x! (12 - x)!].

7. Explicitly compute the probabilities in the previous exercise to verify the following table:

Number Selected   Probability
1 0.017414
2 0.063852
3 0.141894
4 0.212841
5 0.227030
6 0.176579
7 0.100902
8 0.042043
9 0.012457
10 0.002491
11 0.000302
12 0.000017

8. Criticize the binomial model for the process of jury selection. Which of the three assumptions in the binomial model may be violated?

9. Sketch the histogram of the probability distribution in Exercises 6 and 7 

10. Calculate the mean and standard deviation of the Number Selected variable.

11. In Horsley's trial, there were no blacks on the jury. Assuming the binomial model above, what is the probability of this event. Do you think that such a probability value indicates racial bias?


References and Resources

1. UCLA Department of Statistics > Case Studies > The Swain Case Summary

2. Emory University School of Law > Horsley v. Alabama, 11th Circuit Court of Appeals > Footnotes

3. Death Penalty Information Center

4. UC Santa Cruz > Sociologist testifies about how to overcome racial bias in jury selection

5. UCLA Department of Statistics > Calculators

6. Balasubramanian Narasimhan's Homepage > Interactive Binomial Site
(NOTE: You must view this applet with a Java-enabled browser.)

7. John C. Pezzullo's Home Page > Binomial Calculator