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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
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 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
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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%). |
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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. |
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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. |
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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 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? |
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Prototype Activity
The prototype activity is a set of short-answer problems that students
would work through with a partner.
Assessment
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This activity is designed to generate
discussion about probability,
randomness, and their role in
decision-making. |
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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. |
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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. |
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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. |
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Editor's note:
Before 11-6-01, the "student's version" of an activity was called the
"prototype".
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