A university has two departments, $X$ and $Y$. The following admission numbers are observed:

Explain why the apparent gender disadvantage disappears when conditioning on department type.

• A. Because conditioning on department removes a confounding effect due to different application shares across departments, so overall rates are weighted averages of within-department rates
• B. Because the observed pattern is due to random sampling error and would vanish with larger samples, so department-specific comparisons are unreliable
• C. Because admissions data are mismeasured at the department level, and aggregating hides the measurement error making the overall rate more accurate
• D. Because the interaction between gender and department indicates effect modification, meaning the causal effect of gender changes sign within departments

Answer: (A)