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Multiple testing · discretion

P-Hacker Simulator

Chase a star. Then count the false alarms.

THE TRUE EFFECT IS ZERO

How many chances do you want?

Each outcome supplies an independent Uniform(0,1) p-value under a true null. This is a simulation of valid null tests, not a fitted regression or a real dataset.

Smallest p · outcome 70.0715
Bonferroni-adjusted p1.0000
Y1: 0.510Y2: 0.818Y3: 0.916Y4: 0.908Y5: 0.310Y6: 0.090Y7: 0.071Y8: 0.640Y9: 0.463Y10: 0.249Y11: 0.563Y12: 0.724Y13: 0.593Y14: 0.507Y15: 0.174Y16: 0.387Y17: 0.175Y18: 0.408Y19: 0.788Y20: 0.804

Experiment 1 · reproducible seed 20268933. Asterisk: unadjusted p < 0.05. The CSV keeps full precision.

The cost of looking.

Exact chance of ≥1 false alarm64.2%
False-alarm families · 2,000 simulations1291 / 2,000
With Bonferroni · same simulations103 / 2,000

For m independent null tests at 0.05, the chance of at least one rejection is 1 − 0.95ᵐ. Bonferroni compares each p-value with 0.05/m and controls family-wise error even without independence. The exact curve here assumes independence.

Plan primary outcomes, disclose every analysis and treat unplanned searches as exploration. A small p-value alone does not establish a causal effect.

Read the method: J-PAL · Data analysis ↗
Read the method: American Statistical Association · Statement on p-values (2016) ↗
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