INTRODUCTION

The University of California,Berkeley, in 1973 faced a lot of backlash due to the accusation of having gender bias in its admission for its graduate program. The data showed that women in the graduate program were disproportionately rejected at a much higher rate than the male students, at first glance. The data come from the university’s six largest programs. When the data was broken down and analyzed from a different perspective, it told a completely different story.

The figure below shows the overall admission outcomes for all applicants both male and female.

Figure 1.

Take a Deeper look.

Although the overall data can give the illusion that women were admitted at a drastically lower rate than men, it doesn’t give us the whole story. When we break down the data by gender and department.We see a completely different picture.

The first plot is comparing admission by gender, and the second graph is comparing admission by department.The third graph shows admission by gender within each specific department, and the pivot table summarizes the overall data in a table form.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

The graphs show and prove that women were more susceptible to apply to more competitive graduate departments at the University of California Berkeley. These departments had lower admission rates explaining why the overall data showed those results. Male students on the other hand typically applied to Graduate programs with higher admission rates. When we take a look at the graph that depicts admission for male and female students within each department (figure 3). We can see that women were admitted at the same or even higher rate than men.

Simpson Paradox

The Simpson Paradox is a phenomenon that happens when a trend appears in a data set, but when the data is broken down and groups are combined, the trend either reverses or disappears and a new story is told. A lurking variable is a variable that is not particularly included in the analysis of a data set, but plays an important role. This variable can make the data misleading if it’s not properly accounted for. In the specific case, the lurking variable is the department variable.

The UC Berkeley case illustrates Simpson’s paradox best. The overall data showed that women were rejected at a higher rate than their male classmates. If we observe the data on a deeper level and break down the data by department, it is evident that women were admitted at the same or even a greater percentage compared to men. The paradox appears because women were more likely to apply to graduate departments that had a lower acceptance rate. This made the overall numbers appear discriminatory against women.

Works Cited

Wikipedia contributors. “Simpson’s paradox.” Wikipedia, The Free Encyclopedia, Wikimedia Foundation, 18 Aug. 2025, https://en.wikipedia.org/wiki/Simpson%27s_paradox. Accessed 16 Sept. 2025. Simpson, Edward H. “The Interpretation of Interaction in Contingency Tables.” Journal of the Royal Statistical Society, Series B (Methodological), vol. 13, no. 2, 1951, pp. 238–241. Bickel, Peter J., et al. “Sex Bias in Graduate Admissions: Data From Berkeley.” Science, vol. 187, no. 4175, 1975, pp. 398–404. https://doi.org/10.1126/science.187.4175.398. Yule, George Udny. “Notes on the Theory of Association of Attributes in Statistics.” Biometrika, vol. 2, no. 2, 1903, pp. 121–134. https://doi.org/10.2307/2331514. Blyth, Colin R. “On Simpson’s Paradox and the Sure-Thing Principle.” Journal of the American Statistical Association, vol. 67, no. 338, 1972, pp. 364–366. Pearl, Judea, and Dana Mackenzie. The Book of Why: The New Science of Cause and Effect. Basic Books, 2018. Ellenberg, Jordan. How Not to Be Wrong: The Power of Mathematical Thinking. Penguin Books, 2014. Schneps, Leila, and Coralie Colmez. Math on Trial: How Numbers Get Used and Abused in the Courtroom. Basic Books, 2013.