In: Statistics and Probability
Simpson's Paradox, Wage Discrepancy: Here is a
fictitious example where an average across categories conflicts
with the averages obtained within categories. This is called
Simpson's Paradox.
Suppose you own a contracting company and employ 16 people (8 males
and 8 females). Your employees are paid on an hourly basis and the
wages (in dollars per hour) are given in the table below. You are
accused of discriminatory pay practices because the average wage
for the males ($32.50 per hour) is greater than the average wage
for the females ($28.50 per hour).
Gender | . | less than 5 years | . | more than 5 years | . | average | ||||||||
. | of experience | . | of experience | . | (mean) | |||||||||
Male | . |
|
|
32.50 | ||||||||||
Female | . |
|
|
28.50 | ||||||||||
(a) Within the category of less than 5 years of
experience, calculate the average hourly rate for the males
and the females. Round your answer to 2 decimal
places.
For males with less than 5 years of experience,
xmale =
$ per hour.
For females with less than 5 years of experience,
xfemale =
$ per hour.
(b) Within the category of more than 5 years of
experience, calculate the average hourly rate for the males
and the females. Round your answer to 2 decimal
places.
For males with more than 5 years of experience,
xmale =
$ per hour.
For females with more than 5 years of experience,
xfemale =
$ per hour.
(c) Within each category, who has the higher average?
femalesmales
(d) What caused the discrepancy between the over-all male/female
averages and those found within each category?
Workers with more than 5 years of experience get paid more.There were more males with over 5 years of experience. There were not many females with more than 5 years of experience.All of these contributed to the discrepancy.
Additional Materials
Answer :
Given data is :
Gender | Less than 5 years | More than 5 years |
Male | 24,26 | 33,33,35,35,37,37 |
Female | 22,24,27,27,28,28 | 35,37 |
a)Based on these values,
Average hourly rate for male less than 5 years = (24 + 26) / 2
= 50 / 2
= 25
Average hourly rate for male less than 5 years = = $ 25
Now,
Average hourly rate for female less than 5 years = (22 + 24 + 27 + 27 + 28 + 28) / 6
= 156 / 6
= 26
Average hourly rate for female less than 5 years = = $ 26
b)Average hourly rate for male more than 5 years = (33 + 33 + 35 + 35 + 37 + 37) / 6
= 210 / 6
= 35
Average hourly rate for male more than 5 years = = $ 35
Now,
Average hourly rate for female more than 5 years = (35 + 37) / 2
= 72 / 2
= 36
Average hourly rate for female more than 5 years = = $ 36
c)Comparing these two category female has the higher average salary than male.
d)The discrepancy between the over-all male/female averages and those found within each category is :
All of these contributed to the discrepancy.