What is the Simpson’s Paradox?

The Simpson’s Paradox can be defined as “a statistical phenomenon where an association between two variables in a population emerges, disappears or reverses when the population is divided into subpopulations” (Stanford Encyclopedia of Philosophy). In 1973, The University of Calfornia, Berkeley was sued for gender discrimination in that more male students were accepted into the graduate program compared to their female counterparts. Out of 4,526 applicants in this study, 2,691 were male and 1,835 were female.

Was There a Case for Discrimination?

According to the graph above, the percentage of male students who were accepted in the graduate program is higher than the percentage of female students. The graph would prove that there is some form of gender discrimination at play.

However, this graph combines data from six departments.

When splitting the data into six departments, Departments A, B, D and F accepted female students at a higher rate than male students.

Another graph shows that Departments C and E had more female applicants accepted than male applicants.

Conclusion

When looking at the University of California Graduate Admissions Data from 1973, there is an argument for gender discrimination in the application process. However, when looking further into the data by department, the original claims of gender discrimination are less apparent. The Simpson’s Paradox can change the story in how data is analyzed and studied.

Works Cited

Sprenger, Jan and Naftali Weinberger, “Simpson’s Paradox”, The Stanford Encyclopedia of Philosophy (Summer 2021 Edition), Edward N. Zalta (ed.), URL = https://plato.stanford.edu/archives/sum2021/entries/paradox-simpson/.

Wikipedia contributors. (2025, August 18). Simpson’s paradox. In Wikipedia, The Free Encyclopedia. Retrieved 22:31, September 12, 2025, from https://en.wikipedia.org/w/index.php?title=Simpson%27s_paradox&oldid=1306522762