UCBAdmissions dataset in base R. Female and male admitted or rejected from the 6 largest departments at Berkeley, 4526 students applied to Berkeley in 1973.

• 44.5% of male applicants were accepted into Berkeley, as opposed to 30.4% of female applicants

gg_bar <- ucb_tidy_aggregated %>% ggplot(aes(x = Gender, y = prop, fill = Gender)) + geom_col() + geom_text(aes(label = percent(prop)), vjust = -1) + labs(title = "Acceptance rate of male and female applicants", subtitle = "University of California, Berkeley (1973)", y = "Acceptance rate") + scale_y_continuous(labels = percent, limits = c(0, 0.5)) + guides(fill = FALSE)

• Men were more likely to be admitted into Departments C and E, women were more likely to be admitted into the other departments
• 108 women, 825 men applied to Department A

gg_bar_faceted <- ucb_by_dept %>% ggplot(aes(Gender, prop, fill = Gender)) + geom_col() + geom_text(aes(label = percent(prop)), vjust = -1) + labs(title = "Acceptance rate of male and female applicants", subtitle = "University of California, Berkeley (1973)", y = "Acceptance rate") + scale_y_continuous(labels = scales::percent, limits = c(0, 1)) + facet_wrap(~Dept) + guides(fill=FALSE)

• Simpson's paradox: effect of gender disappears when control for the effect of department on admission %. No campus-wide bias against applicants of either gender.
• bias != discrimination