Simpson's paradox: A statistician's case study.

Area of Science:

• Social Sciences
• Statistics
• Higher Education

Background:

• Gender equality and workforce diversity are key topics in higher education discussions.
• Observed differences between groups can be misleading due to unrecognised third variables.
• Simpson's Paradox describes this statistical phenomenon where aggregate data trends reverse when data is broken down by subgroups.

Purpose of the Study:

• To illustrate Simpson's Paradox using a real-world case study.
• To investigate potential gender bias in graduate school admissions at UC Berkeley in 1973.
• To demonstrate how confounding variables can alter the interpretation of group differences.

Main Methods:

• Analysis of graduate school admissions data from UC Berkeley for 1973.
• Comparison of overall admission rates between male and female applicants.
• Re-examination of admission rates stratified by individual academic departments.

Main Results:

• Overall, males were 1.8 times more likely to be admitted than females, suggesting gender bias.
• When analyzed by department, women had higher admission rates than men in four out of six departments.
• The confounding variable, 'department,' showed a strong association with both admission rates and gender application patterns.

Conclusions:

• The initial observation of gender bias was a paradox caused by the confounding effect of the academic department.
• Females tended to apply to departments with lower overall admission rates.
• Understanding confounding variables is crucial for accurately explaining differences between groups and avoiding erroneous conclusions.