Question

Simpson's Paradox, Wage Discrepancy: USE SOFTWARE 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 ($32.25 per hour) is greater than the average wage for the females ($27.75 per hour).

Gender	.	less than 5 years	.	more than 5 years	.	average
	.	of experience	.	of experience	.	(mean)
Male	.	23, 25		33, 33, 35, 35, 37, 37		32.25
Female	.	21, 23, 26, 26, 27, 27		35, 37		27.75

(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,

x_male = $ per hour.

For females with less than 5 years of experience, x_female =$ 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,

x_male = $ per hour.

For females with more than 5 years of experience,

x_female = $    per hour.

(c) Within each category, who has the higher average?

females

males    

(d) What caused the discrepancy between the overall 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.

Answer 1

a) Within the category of less than 5 years of experience:

Average hourly rate for males = (23 + 25)/2 = 24

Average hourly rate for females = (21 + 23 + 26 + 26 + 27 + 27)/6 = 25

xmale = $24 per hour

xfemale = $25 per hour (more than males)

b) Within the category of more than 5 years of experience:

xmale = $35 per hour

xfemale = $36 per hour (more than males)

c) Within each category, females have the higher average hourly rate.

d) The discrepancy between the overall averages and the category averages is because that there are many males in more than 5 years-experience category (Option B) which have a higher category average (Option A), hence they contribute a lot in the overall average. Also, as there are less females with more than 5 years of experience, they contribute less to the overall mean and hence the discrepancy is caused (Option C).

Hence, all of these contributed to the discrepancy. D) option is correct