Simpson's paradox: A statistician's case study

Gender equality and workforce diversity has recently been in the forefront of College discussions. Reasons for the difference between various groups may not be as they initially appeared. The results of comparing the outcome between two groups can sometimes be confounded and even reversed by an unrecognised third variable. This concept is known as Simpson's Paradox, and is illustrated here using a renowned case study on potential gender bias for acceptance to Graduate School at the University of California, Berkeley.  The investigation showed that males were 1.8 times more likely to be admitted to Graduate School than females in 1973. Initially it appeared that women were discriminated against in the selection process. However, when admissions were re-examined at individual Departments of the School, admission tended to be better for women than men in four of six Departments. This contradiction or paradox tells us that the association between admission and gender was dependent upon on Department.  The confounding effect of Department was defined by two characteristics. Firstly, a strong association between Department and admission: some Departments admitted much smaller percentages of applicants than others. Secondly, a strong association between Department and gender: females tended to apply to Departments with lower admission rates.  The explanation of differences between groups can be multifactorial. A search for possible confounders will assist in this understanding. This could apply whenever two groups initially appear to differ, but on closer analysis this difference is either unfounded, or even reversed by reference to a third, confounding variable.