Lack of Control Leads to Bias

Based on the admission rates by major and gender, there is no visible bias remaining (except in major A, in favor of women!)
The feature of the study that leads to confusion is lack of control of who gets which treatment.
- Treatment is "which major to apply to," not the outcome of "admitted or not").
Major determines admission rate, but gender determines major. The indirect cause and effect relationship between gender and admission rate (via choice of major) is confounded with the direct causal relationship of major to admission rate.
Frequency of mediating variables (like choice of major) is crucial, but the effect is concealed by taking averages.