Make a prediction first
If a single test has a 5% chance of a false positive, what’s the chance that at least one of 20 independent tests gives a false positive, even though nothing real is going on in any of them? Guess a number, then check it below.
Exact probability of at least one false positive: 64.2%
Per-test alpha that would keep the overall rate at your chosen alpha (Bonferroni correction): 0.00250
Click "Run simulation" to see a Monte Carlo estimate here.
What changed and why
The exact figure and the Bonferroni-corrected alpha update instantly as you change the number of tests or alpha — both are closed-form formulas, not simulations. The Monte Carlo estimate only updates when you click “Run simulation”: it actually generates the requested number of simulated batches, in a background worker, and reports what fraction had at least one test cross the threshold by chance, alongside the estimate’s standard error.
Each simulated “test” here is a uniform random draw standing in for a p-value under the null hypothesis — there is, by construction, no real effect anywhere in the simulation. Any “significant” result the simulation finds is, by definition, a false positive.
Model assumptions
- Every test is treated as independent of every other one.
- There is no real effect anywhere in the simulation — every positive result is, by construction, a false positive.
- “Significant” means any single test crossing alpha, which is precisely the undisciplined practice this page exists to make visible — a properly planned analysis would decide its comparisons and corrections in advance.
Reproducibility
Every run is seeded with the same documented generator (mulberry32) used throughout this site’s interactives, so the same number of tests, alpha, trial count, and seed always reproduce the same estimate. Clicking “Run simulation” updates this page’s URL with your parameters, so a specific setup can be shared as a link.
Sources and method
The Bonferroni correction shown here — dividing your target alpha by the number of tests — follows the original treatment in the statistics literature.(Dunn, 1961) See Multiple opportunities and selection effects for the plain-language explanation and the real-world caveat this model leaves out: actual “opportunities” for a coincidence are rarely as cleanly independent as the tests simulated here.