How to use regression to study pay discrimination (1)

This is the first in a series of
posts about the use of regression
analysis to measure pay discrimination
between two groups of workers
(group 1 and group 2). (Knowledge
of the basic idea of regression analysis
is needed for this series).

The first step is measuring the difference
in average pay (group 1 average minus
group 2 average). The next step is to
conduct a regression analysis with
each observation representing one worker,
the dependent variable is the pay, and
the independent variable is an indicator
variable that equals 0 if the worker
is group 1 and 1 if the worker is group 2.
(For a dumb historical reason, this
type of indicator variable is also
called a dummy variable.)

Here is an example of this type of
regression.

pay = -4* group + 20.75
r-squared= 0.06816

The coefficient -4 indicates that there
is pay disparity between the groups.

The pattern can be illustrated by showing the
frequency distribution–the number of workers
in each group (shown in each column) and the
number of workers in each job category (shown
in each row). Next to the frequency count
is the average pay for each category.
In this case, there are 16 workers
in two groups and four job categories:

            frequency               avg. pay
          group1 group2  Total    group1 group2
jobcat 1      2      2       4       12    8
jobcat 2      2      2       4       17   13
jobcat 3      2      2       4       22   18
jobcat 4      2      2       4       32   28
TOTAL         8      8      16

averages:
group 1:  166/8.0=   20.7500
group 2:  134/8.0=   16.7500
difference of averages:     4.0000

Note that the regression coefficient (4) is the
same as the difference in average pay.

See the spreadsheet at this link:

http://myhome.spu.edu/ddowning/fos/discrgr.xlsx
which shows how this is translated into the
data matrix of 1’s and 0’s.

to be continued

……………..
–Douglas Downing
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