On the Gender Gap

It is all to easy to lie using statistics, but by using proper analysis, you can find the real truth behind facts. One particular area that I find overblown with the use of possibly misleading statistics is the discussion of the gender gap in wages that exists within our society. This gender gap, it is argued, is a result from the discrimination against women in the work place; however, those who argue for this discrimination often do not look closely enough at the facts.

The website RateMyProfessor.com has gone a long way to assisting students in determining which classes to take based on the positive or negative characteristics of the professor. However, it apparently has also gone a long way to assisting students in venting their unconscious biases toward women. In the New York Times article Is the Professor Bossy or Brilliant? Much Depends on Gender, Claire Cain Miller examines a new interactive chart based on the posts of the RMP website. She concludes:

The chart makes vivid unconscious biases. The implications go well beyond professors and college students, to anyone who gives or receives feedback or performance reviews. It suggest that people tend to think more highly of men than women in professional settings, praise men for the same things they criticize women for, and are more likely to focus on a woman's appearance or personality and on a man's skills and intelligence.

As this her findings flowed from her analysis of an interactive chart published by Benjamin Schmidt, I decided to play around with the data myself. Using the word "bossy", which is not only highlighted in the title of the article, but was a point of emphasis on Sheryl Sandburg's book Lean In. The chart reveals (below) that yes, there appears to be a gender bias with the negatively connoted word "bossy". However, the issue I take with this apparent bias is the scale to which this bias is present. The use of this word is listed in uses per million; even in the most prevalent case of disparity in the use of the word "bossy" (computer science), there is only a difference of about 1.8 uses per million. It doesn't seem reasonable that a difference in 0.00018% of words used can be statistically significant. Even looking at more common words, such as "brilliant" (cited by author, difference in ~0.0072%) or "best" (difference in 0.0484%), reveal that, while these words are skewed toward males, it may be difficult to call them statistically significant.

Apart from statistical significance, ignoring specific confounding factors can lead to an overestimation of the gender gap in earnings. A recent article from the Michigan Daily analyzed the gap in wages between men and women at twelve top public universities. According to their analysis:

Calculations show that the average disparity between female and male salaries at these 11 top colleges and the University [of Michigan] shows that women earn 96 cents for every dollar a man makes—3.4 percent less. Furthermore, these top universities fill their most prominent positions with mostly men. Analysis revealed that 37 percent of executive employees were female. Sixty-three percent were men.

Lack of a large sample size notwithstanding, the 3.4% difference between men's and women's earnings can easily be explained by factors other than gender biases. It is unclear if the data cited is based on a median value of men and women, but if it is in fact, the data can be skewed toward higher male wages based on the mix of employment (i.e. males as President's/Athletic Directors, females as Provosts/Vice Presidents).