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The Role of Probability in Discrimination Cases

James J. Higgins
Department of Statistics
Kansas State University
101 Dickens Hall
Manhattan, KS 66506

Statistics Teaching and Resource Library, August 21, 2001

© 2001 by James J. Higgins, all rights reserved. This text may be freely shared among individuals, but it may not be republished in any medium without express written consent from the author and advance notification of the editor.

An important objective in hiring is to ensure diversity in the workforce. The race or gender of individuals hired by an organization should reflect the race or gender of the applicant pool. If certain groups are under-represented or over-represented among the employees, then there may be a case for discrimination in hiring. On the other hand, there may be a number of random factors unrelated to discrimination, such as the timing of the interview or competition from other employers, that might cause one group to be over-represented or under-represented. In this exercise, we ask students to investigate the role of randomness in hiring, and to consider how this might be used to help substantiate or refute charges of discrimination.

Key words: Probability distribution, binomial distribution, computer simulation, decision rules


The activity allows students to get a feel for random variability and probability through simulation, and then to apply what they learn to an important decision-making problem.

Activity Description

A company decides to hire 14 people. The applicant pool is large, and there are equal numbers of equally qualified women and men in the pool. To avoid claims of discrimination, the company decides to select the prospective employees at random. Students should consider three questions. (1) How big a difference between the numbers of men and women who are hired might occur just by chance? (2) How likely is it that equal numbers of men and women are hired? (3) How big a difference might suggest discrimination in hiring?

An attached Excel program simulates the hiring process. Given the large size of the applicant pool, the selection process is modeled as a sequence of 14 Bernoulli trials with p = .5 where p is the probability that a hire is a female. Instructions are provided with the Excel spreadsheet on how to use the program.

Teaching Notes
Students should discover a rule that would cause them to suspect discrimination. For instance, one such rule might be that if there are 11 or more men hired, or 11 or more women hired, then this might be indicative of discrimination. Students should also discover that having exactly 7 men and 7 women hired has a relatively small chance of happening (only about a 21%).
By discussing the consequences of different decision rules, the student can be introduced to the notion of errors in hypothesis testing. Suppose, for instance, that a regulatory agency were to investigate possible discrimination if the disparity between genders of newly hired employees is 11 to 3. What is the chance that a fair employer would be investigated for discrimination? Compare this to an agency that would investigate if the disparity were 10 to 4 or 9 to 5.
The instructor may adapt this exercise to go along with a discussion of the binomial distribution. If this is done, then a table of the binomial distribution could be used to describe the probability distribution of the number of women (or men) hired by the company.
Students should be invited to make the connection between this problem and other problems that appear to be different but have the same probability structure. Here is an example. ďA standard treatment for a certain disease has a 50-50 chance of working. A new treatment is proposed and is tried on 14 patients. How many patients would have to benefit from the new treatment before you would be reasonably sure that it is better than the old treatment?

Prototype Activity

The prototype activity is a set of short-answer problems that students would work through with a partner.


This activity is designed to generate discussion about probability, randomness, and their role in decision-making.
Assessment should come in the form of short answers to questions on an activity such as the prototype activity and class discussion. Donít expect students to immediately grasp the ideas. It will take time and lots of examples.
Class discussion should follow along the lines of what is suggested in the Teaching Notes. Students should be able to draw parallels between this problem and similar problems involving probability and randomness.
With this activity, the student should begin to get an intuitive feel for random variability, and they should begin to appreciate the role that probability can play in decision-making.

Editor's note: Before 11-6-01, the "student's version" of an activity was called the "prototype". 



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