Question

Simpson's Paradox, Wage Discrepancy: Here is fictitious example where an average across categories conflicts with the averages obtained within categories. This is called Simpson's Paradox.

The manager at the GARP clothing branch in the mall is applauded for treating male and female sales representatives equally with respect to pay. This is demonstrated by the averages given in the table below. The average (mean) of the 6 males is $16.00/hour which equals the average for the 7 females. We will look at the data but refine our focus to include average pay within the categories of assistant and associate sales positions.

Gender     

.

Assistant Sales

.

Associate Sales

.

average

.

representatives

.

representatives

.

(mean)

Male

.

14,

14,

15,

16

18,

19

16.00

Female

.

13,

14

15,

16,

17,

18,

19

16.00

(a) Within the category of Assistant Sales Representatives calculate the average hourly rate for the males and the females. Round your answer to 2 decimal places.
Average wage for male assistant sales reps:

x_male =

$  per hour.
Average wage for female assistant sales reps:

x_female =

$  per hour.

(b) Within the category of Associate Sales Representatives calculate the average hourly rate for the males and the females. Round your answer to 2 decimal places.
Average wage for male associate sales reps:

x_male =

$  per hour.
Average wage for female associate sales reps:

x_female =

$  per hour.

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

femalesmales    

(d) How did the pay differences between males and females within each category get hidden in the over-all averages?

Associate sales representatives get paid more (on average).There were fewer male associate sales representatives.    There were more female associate sales representatives.All of these contributed to the pay differences being hidden in the over-all averages.

Answer 1

(a) Average wage for male assistant sales reps:

x_male = $ 14.75 per hour.
Average wage for female assistant sales reps:

x_female = $ 13.5 per hour.

(b) Average wage for male associate sales reps:

x_male = $ 18.5 per hour.
Average wage for female associate sales reps:

x_female = $ 17 per hour.

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

males    

(d) How did the pay differences between males and females within each category get hidden in the over-all averages?

All of these contributed to the pay differences being hidden in the over-all averages.