# Revisiting the Berkeley Admissions data: Statistical Tests for Causal Hypotheses

arXiv: https://arxiv.org/abs/2502.10161 · HTML: https://mlsanity.com/paper/2502.10161/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 38 references that are in the map.
- First posted on arXiv 14 Feb 2025.

## Builds on (most cited first, 19 of 19)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [Avoiding Discrimination through Causal Reasoning](https://mlsanity.com/paper/1706.02744/) (2017)
- [Path-Specific Counterfactual Fairness](https://mlsanity.com/paper/1802.08139/) (2018)
- [Fair Inference On Outcomes](https://mlsanity.com/paper/1705.10378/) (2017)
- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [50 Years of Test (Un)fairness: Lessons for Machine Learning](https://mlsanity.com/paper/1811.10104/) (2018)
- [A causal framework for discovering and removing direct and indirect discrimination](https://mlsanity.com/paper/1611.07509/) (2016)
- [Causal Fairness Analysis](https://mlsanity.com/paper/2207.11385/) (2022)
- [The Sensitivity of Counterfactual Fairness to Unmeasured Confounding](https://mlsanity.com/paper/1907.01040/) (2019)
- [On the Testability of Causal Models with Latent and Instrumental Variables](https://mlsanity.com/paper/1302.4976/) (2013)
- [The Inflation Technique for Causal Inference with Latent Variables](https://mlsanity.com/paper/1609.00672/) (2016)
- [Causal Fairness under Unobserved Confounding: A Neural Sensitivity Framework](https://mlsanity.com/paper/2311.18460/) (2023)
- [Instrumentality Tests Revisited](https://mlsanity.com/paper/1301.2258/) (2013)
- [On falsification of the binary instrumental variable model](https://mlsanity.com/paper/1605.03677/) (2016)
- [Foundations of Structural Causal Models with Latent Selection](https://mlsanity.com/paper/2401.06925/) (2024)

## Abstract (arXiv)

Reasoning about fairness through correlation-based notions is rife with pitfalls. The 1973 University of California, Berkeley graduate school admissions case from Bickel et. al. (1975) is a classic example of one such pitfall, namely Simpson's paradox. The discrepancy in admission rates among males and female applicants, in the aggregate data over all departments, vanishes when admission rates per department are examined. We reason about the Berkeley graduate school admissions case through a causal lens. In the process, we introduce a statistical test for causal hypothesis testing based on Pearl's instrumental-variable inequalities (Pearl 1995). We compare different causal notions of fairness that are based on graphical, counterfactual and interventional queries on the causal model, and develop statistical tests for these notions that use only observational data. We study the logical relations between notions, and show that while notions may not be equivalent, their corresponding statistical tests coincide for the case at hand. We believe that a thorough case-based causal analysis helps develop a more principled understanding of both causal hypothesis testing and fairness.