Here’s one more example of the regression analysis
of pay discrimination. The same regressions that were
presented in the previous examples will be applied to
this example.
pay = 3.218 group + 28.393 r-squared= 0.02603
The regression coefficient and the data table show that
group 2 average pay exceeds group 1 average pay by 3.218:
frequency avg. pay
group1 group2 Total group1 group2
jobcat 1 19 8 27 16 12
jobcat 2 15 17 32 25 22
jobcat 3 18 25 43 36 31
jobcat 4 9 40 49 45 40
TOTAL 61 90 151
averages:
group 1: 1732.0000/61.0= 28.3934
group 2: 2845.0000/90.0= 31.6111
difference of averages: -3.2177
However, when the regression analysis includes the
job categories as the independent variables, the
coefficient not only changes, it reverses sign:
pay = 9.604 ind2 + 19.508 ind3 + 28.347 ind4 - 4.313 group + 16.092 r-squared= 0.99843
Observing the frequency table above, we can see
that group 2 members are actually paid less than
group 1 members in every job category. The only
reason that the average pay for group 2 is higher
than for group 1 is because the members of group 2
are more likely to be in the higher-paid jobs.
This example makes it especially clear why it is
crucial to look at job category data to determine
discrimination. In some cases, failling to include
this data might totally conceal the actual pay
discrimination.
See the spreadsheet at this link:
http://myhome.spu.edu/ddowning/fos/discrgr.xlsx
……………..
–Douglas Downing
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