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# Beyond the four fifths rule: significance, power and uncertainty in adverse impact analysis

Research paper · 16 pages · Published 2026-10-21 · By Holistic AI

NYC Local Law 144 requires impact ratios but no significance test, no interval and no threshold, so a published ratio says nothing about its own reliability. This paper sets out the statistics that close that gap and uses simulation to show when the four fifths rule, the Z test and Fisher's exact test can be trusted. It ends with a practical reporting standard: ratio, interval, test and sample size for every comparison.

## Key numbers

- **38%**: Null samples flagged by the four fifths rule at 10 applicants per group
- **859**: Applicants per group for 80% power to detect a true ratio of 0.80
- **80%**: Chance of a false intersectional flag across 13 unadjusted tests
- **4**: Things every audit comparison should report: ratio, interval, test and n

## What is inside

- The legal texts: Uniform Guidelines, EEOC Q and A, Castaneda and Hazelwood
- Formulas and reference code for Z, Fisher, Katz intervals and Bayesian estimates
- Simulations of false positives and detection for each decision rule
- Intersectional multiple comparisons with Holm and Benjamini Hochberg
- Power tables, three worked examples and a reporting standard

## Who it is for

- Data scientists and IO psychologists
- Bias auditors and HR analytics teams
- Employment counsel and their experts

The full PDF is free. Request it with the form at https://www.nycbiasaudit.com/resources/adverse-impact-statistics-beyond-four-fifths.

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Holistic AI carries out independent Local Law 144 bias audits. What the service includes: https://www.nycbiasaudit.com/services.md. To commission a bias audit or ask a question, book a call at https://www.nycbiasaudit.com/demo or email we@holisticai.com.