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It’s Not Always Discrimination

23-year-old Ciera Pekarcik, Miss Utah

23-year-old Marissa Powell, Miss Utah USA

There has been much made of the apparent pay discrepancies between men and women.  At the recent Miss America Pageant, Nene Leakes posed the question,

A recent report shows that in 40% of American families with children women are the primary earners, yet they continue to earn less than men.  What does this say about society?”

Miss Utah took a lot of flak for her poor response to the question.  But sometimes we need to look a bit deeper at these questions, and the answers aren’t always so straightforward as to quote a simple statistic.  I’ve been reading Superfreakonomics by Stephen Dubner and Steve Levitt, and as usual they make some interesting points that are often against conventional wisdom.  In analyzing the pay gap among men and women, they find some reasons that aren’t necessarily sexist.  Among women with an MBA, the pay gap can be explained by the following reasons.

  • “Women have slightly lower GPAs than men and, perhaps more important, they take fewer finance courses.  All else being equal, there is a strong correlation between finance background and career earnings.

  • Over the first fifteen years of their careers, women work fewer hours than men, 52 hours per week versus 58.  Over fifteen years, that six-hour difference adds up to six months’ less experience.

  • Women take more career interruptions than men.  After ten years in the workforce, only 10 percent of male MBAs went for six months or longer without working, compared to 40 percent of female MBAs.

The big issue seems to be that many women, even those with MBAs, love kids.  The average female MBA with no children works only 3 percent fewer hours than the average male MBA.  But female MBAs with children work 24 percent less.  “The pecuniary penalties from shorter hours and any job discontinuity are enormous,” the three economists write.  “It appears that many MBA mothers, especially those with well-off spouses, decided to slow down within a few years following their first birth.”

There’s one more angle to consider when examining the male-female wage gap.  Rather than interpreting women’s lower wages as a failure, perhaps it should be seen as a sign that a higher wage isn’t as meaningful an incentive for women as it is for men.  Could it be that men have a weakness for money just as women have a weakness for children?

So, in answer to Leakes question to Miss Utah, rather than the “obvious” answer that society discriminates against women, perhaps it says that society rewards people who don’t take time off work.

Here’s an example that I use when I teach introductory statistics classes to show that statistics can be paradoxical.  A university offers 2 degree programs: electrical engineering and English.  Admission is competitive, and women expect discrimination.  Is it fair to conclude discrimination?

We can see that more males apply, but when we look at the rates of admission, it appears that males are admitted at a higher rate.

Male

Female

Admit

35

20

Deny

45

40

Totals

80

60

Percent Admitted

43.8%

33.3%

It looks like discrimination is going on.  But is this a fair test?  At this point I will illustrate to students how to perform a Chi-Square test, and when we are through with out calculations, the Chi-Square test shows that there is no difference in admission between men and women.  It is at this point that I like to quote Mark Twain:  “There are liars, damn liars, and statisticians.”

The simpler calculation seems to show that there is discrimination, but the more complex calculation shows that there isn’t.  So which one do we believe?  Well, perhaps there is discrimination going on in one of the departments, so let’s looks at each department and see if we can figure out where the discrimination is going on.

Engineering

Male

Female

Admit

30

10

Deny

30

10

Total

60

20

In the Engineering Dept, we can see that the admission rate is 50% for both genders.  Now let’s check the English Dept.

English

Male

Female

Admit

5

10

Deny

15

30

Total

20

40

Well, there’s no discrimination between genders here either.  Men and women are admitted at a rate of 25%.

This is an example of what we call Simpson’s Paradox.  We can see that there is no discrimination going on in either department.  So why did there appear to be discrimination in the first table shown?  The reason for this paradox is that the 2 groups are unequally sized.  Because the number of men is larger than women (especially in the Engineering department), those numbers overwhelm the smaller numbers in the English Department, giving us a false impression of discrimination.  Therefore the Chi-Square test is the better test than the simple admission calculation.  There is no discrimination going on.

This example is based on a real-life lawsuit filed at the University of California-Berkeley.  (If you would like to learn how to perform the calculation using a free stats package called R, here is a tutorial.)  Women cited as fact that they were being admitted at a lower rate than men.  However, when they looked at each department to determine where the discrimination was actually happening, they found that women were actually admitted at a HIGHER rate than men.  Once again, it was a trick of the numbers that there were more male applicants than female.

So contrary to the charge that I have a feminist agenda, I just want data to back up assertions.  Sometimes discrimination isn’t quite so clear cut, but sometimes it really is discrimination.  I wish Simpson was here to cut through all the paradoxes that can be found in statistics, but we shouldn’t be quite so cynical as Mark Twain was.  Sometimes we have to do a more complex statistical test to know the real answers, or we have to cut through erroneous assumptions.  Comments?

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