Data from UC Berkeley's 1973 graduate admissions across five departmentnts, with 3,593 individual applicant records. This is the classic dataset used to demonstrate Simpson's paradox in the context of logistic regression: the overall association between gender and admission appears to show bias against women, but this effect reverses or disappears when controlling for departmentnt. The departmentnt identifiers are anonymized.
Format
A tibble with 3,593 rows and 3 columns:
- department
Department identifier. Type: numeric. Values: 1, 2, 3, 4, 5. Five anonymized departmentnts that differ in their admission rates and gender composition of applicants.
- female
Sex of applicant. Type: numeric. Binary indicator (0/1) where 1 = female, 0 = male. Approximately 48% of applicants are female.
- admitted
Admission decision. Type: numeric. Binary indicator (0/1) where 1 = admitted, 0 = not admitted. Overall admission rate is 32%.
Source
Bickel, P. J., Hammel, E. A., & O'Connell, J. W. (1975). Sex
bias in graduate admissions: Data from Berkeley. Science, 187(4175),
398-404. Original data file: berkeley.dta
Details
This dataset is used in Chapters 10-11 (Multiple Logistic Regression and Model Fit/Diagnostics) to illustrate confounding in logistic regression and Simpson's paradox. Key analyses include: computing odds ratios for admission by gender within and across departmentnts, fitting multiple logistic regression models with departmentnt as a control variable, performing likelihood ratio tests, and chi-squared goodness-of-fit tests.
Note that this dataset uses female as the gender indicator (1 =
female), whereas berk_sub uses male (1 = male). The
departmentnt variable is coded numerically (1-5) rather than by departmentnt
name.
Examples
data(berkeley)
head(berkeley)
#> # A tibble: 6 × 3
#> department female admitted
#> <int> <int> <int>
#> 1 1 0 0
#> 2 1 1 0
#> 3 2 0 0
#> 4 2 1 0
#> 5 3 0 0
#> 6 3 1 0
# Unadjusted model: gender only
glm(admitted ~ female, data = berkeley, family = binomial)
#>
#> Call: glm(formula = admitted ~ female, family = binomial, data = berkeley)
#>
#> Coefficients:
#> (Intercept) female
#> -0.5424 -0.4472
#>
#> Degrees of Freedom: 3592 Total (i.e. Null); 3591 Residual
#> Null Deviance: 4511
#> Residual Deviance: 4472 AIC: 4476
# Adjusted model: controlling for departmentnt
glm(admitted ~ female + factor(department), data = berkeley, family = binomial)
#>
#> Call: glm(formula = admitted ~ female + factor(department), family = binomial,
#> data = berkeley)
#>
#> Coefficients:
#> (Intercept) female factor(department)2
#> 0.54418 -0.03069 -1.14008
#> factor(department)3 factor(department)4 factor(department)5
#> -1.19456 -1.61308 -3.20527
#>
#> Degrees of Freedom: 3592 Total (i.e. Null); 3587 Residual
#> Null Deviance: 4511
#> Residual Deviance: 3974 AIC: 3986