Overview
This lecture explores UC Berkeley's 1973 graduate admissions data, focusing on gender differences using categorical data analysis methods to examine potential bias.
Introduction to the Berkeley Admissions Study
- Researchers analyzed 1973 admissions to Berkeley’s six largest graduate departments for gender-related trends.
- Data from that era only included binary gender categories (male and female).
- Only 32% of admitted students were women, raising questions about possible admissions bias.
Organizing and Summarizing Categorical Data
- Admissions data is displayed in a two-way table, categorizing by gender and admissions decision (admitted/rejected).
- Row and column totals, plus a grand total, summarize the distribution.
- A marginal distribution examines the distribution of a single variable, such as the proportion of applicants by gender.
Marginal Distributions: Gender Composition of Applicants
- 59.5% of applicants were male; 40.5% were female.
- More men applied than women, but this alone doesn't fully explain the gap in admitted students.
Visualizing with Graphs
- Side-by-side bar graphs compare applicant and admitted student gender proportions.
- Effective graphs require titles, axis ticks, labels, and keys for clarity and AP exam credit.
Conditional Distributions: Admission Rates by Gender
- Admission rate for males: 44.5%; for females: 30.4%.
- Conditional distributions focus on one subgroup at a time (e.g., among male applicants, what percent were admitted/rejected?).
- Segmented bar charts show proportions admitted/rejected within each gender group.
Interpreting Associations Between Gender and Admission
- Data shows women are admitted at lower rates compared to men.
- A claim of association requires: stating the association, supporting it with comparative percentages, and giving context (mentioning variables).
- Use comparative language like "higher" and "lower" when explaining associations.
Department-Level Analysis
- Departments are categorized as not selective (>50% admitted), selective (26-50% admitted), or very selective (1-25% admitted).
- Within departments, admission rates for women are higher or similar to men.
- Despite this, the overall female admit rate is lower, presenting a statistical paradox.
Discussion and Mosaic Plots
- Mosaic plots visualize segmented bar data, adjusting width for applicant numbers in each category.
- Discussion question: How can women have higher admit rates within departments but a lower overall admit rate?
Key Terms & Definitions
- Two-way table — A table categorizing data by two variables.
- Marginal distribution — The distribution of a single variable in a two-way table.
- Conditional distribution — The breakdown of one variable for a specific subgroup of another variable.
- Segmented bar chart — A bar graph showing subcategory proportions within a category.
- Mosaic plot — A segmented bar chart where bar width represents sample size.
Action Items / Next Steps
- Consider: Why do overall admit rates for women differ from within-department rates? Prepare reasoning for class discussion.
- Review today’s graphs and summary methods for describing categorical data.
- (Optional) Print or complete guided notes available online.