Use case 2 · Power and false-alarm analysis

The four-fifths rule at small-business scale

The pattern

The federal four-fifths rule compares selection rates between groups. With the small applicant pools of a small business, it misfires in both directions.

Question: Can a small business trust the four-fifths rule?
Lane: Hiring
Basis: Federal guidelines, 29 CFR 1607.4(D)

What METRIS does

Compute selection rates and the four-fifths ratio for every screening rule, each month
Pair it with an exact significance test and report both
Pool months until the evidence is strong enough to act on

Four-fifths ratios when there is no bias

Monte Carlo · synthetic data

Both groups truly advance at 50%. With 40 applicants each, chance alone pushes the ratio below 0.8 in 31.2% of pools (exact); a false flag.

Method

impact ratio = min(r_A, r_B) / max(r_A, r_B); flag if < 0.8 Fisher exact test on the 2×2 table, α = 0.05

Selection rates: 50% vs. 50% (no gap) and 50% vs. 35% (gap)
Applicants per group: 10 to 200
Runs: 1,000 per point; 10,000 for the histogram

The four-fifths rule is a screening heuristic from 29 CFR 1607.4(D), not a statistical test. At small scale it needs a test, and a test needs pooled data.

Flags vs. applicants per group

Monte Carlo · synthetic data

With a real gap (50% vs. 35%), Fisher's exact test reaches 80% power only near 200 applicants per group, while the four-fifths rule flags 56% of bias-free pools at 10 per group. Neither alone is enough at small scale.

Reproducibility

Selections are binomial per group; Fisher's exact test from SciPy. Random seed 20261013; Python with NumPy 2.5.3 and SciPy.

Sources

Uniform Guidelines on Employee Selection Procedures, 29 CFR 1607.4(D)

Study design and analysis: Suneeta Modekurty, SANJEEVANI AI

A statistical study of a pattern, not of any event. It identifies no organization or person. Simulated figures use synthetic data; published figures are industry-wide.