
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
underrepresented or overrepresented 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
overrepresented or underrepresented. 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
Objective
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 decisionmaking
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. “A standard
treatment for a certain disease has a 5050 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
shortanswer problems that students would work through with a
partner.
Assessment

This activity is designed to generate
discussion about probability, randomness, and their
role in decisionmaking. 

Assessment should come in the form of short
answers to questions on an activity such as the
prototype activity and class discussion. Don’t 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
decisionmaking.  
Editor's
note: Before 11601, the "student's version" of an
activity was called the "prototype".

