What is gender bias? Gender bias means that one gender is treated in a more or less favorable way, based on gender stereotypes rather than real differences. In the Fall of 1973 UC Berkley in the fear of a gender bias law suit had a statistician review their admission data which significantly showed bias against women applicants. “UC Berkeley’s graduate school had admitted roughly 44% of their male applicants and 35% of their female applicants”1. UC Berkley graduate school admission data showed obvious bias against women.

The figure above, fig 1.1 clearly shows that more male applicants were admitted as compared to the female applicants. Was this another case of gender bias in society? To be able to understand and conclude what was happening a deeper look into the applications for each department that was offered had to be taken. However taking a deeper look into the data by reviewing each department reviewed no bias against female applicants but a small significant bias in favor of the women.

The figure above, fig 1.2 shows that more women were interested in 4 departments, C,D,E, and F and for each department more than half female applicants were admitted to those departments. It goes on to show a higher number of male applicants for department A and B and more than half of the men that applied in those department were not admitted.The figure above, fig 1.2 tells a different story to what first anticipated when they looked at the aggregated data in fig 1.1. There was really no gender bias against female applicants but instead the women had certain preferences in departments and these departments were hard to get enrolled in. “when taking into account the information about departments being applied to, the different rejection numbers reveal the different difficulty of getting into the department, and at the same time it showed that women tended to apply to more competitive departments with lower rates of admission”.2

“Simpson’s Paradox is a phenomenon in probability and statistics in which a trend appears in several groups of data but disappears or reverses when the groups are combined.”3 A lurking variable is a variable that is not included in a statistical analysis, yet impacts the relationship between two variables within the analysis. The UC Berkely 1973 admission scenario is an illustration of Simpsons Paradox because dividing the aggregated data into different departments reversed the trend that appeared when they looked at the combined data.The lurking variable in this Paradox is department.

References:

[1] Tom Grigg. “Simpson’s Paradox and Interpreting Data, Towards Data Science”. Editor Ben Huber Man, December 9, 2018, https://towardsdatascience.com/simpsons-paradox-and-interpreting-data-6a0443516765

[2] Bickel, P. J., Hammel, E. A., & O’Connell, J. W. (1975). Sex bias in graduate admissions: Data from Berkeley. Science, 187(4175), 398–404. http://doi.org/10.1126/science.187.4175.398↩︎

[3] Tom Copleland. ““Simpson’s Paradox and Interpreting Data, Towards Data Science”. Editor Ben Huber Man, July 12 2020,https://towardsdatascience.com/what-is-simpsons-paradox-4a53cd4e9ee2