We simulated 10,000 A/B tests where the two versions were identical. Analyzed once at the end, 5.0% falsely declared a winner — exactly what a 5% significance level promises. Checked 50 times with a stop-at-significance rule, 32.3% declared a winner — 6.5× the promised rate. Run the simulation yourself below.
Both groups have the same true conversion rate (an A/A test), so every "significant" result is a false positive. Choose how often to peek and see what happens to the false-positive rate.
Scenario: each experiment sends 10,000 visitors to A and 10,000 to B, both converting at 5%. You check the running test 10 times (about every 1,000 visitors per group) and stop the moment p < 0.05 — the way most dashboard-watchers actually behave.
Each experiment sent 10,000 visitors to each of two identical variants converting at 5%, and analyzed the running results with a two-proportion z-test at evenly spaced checkpoints, stopping the moment the test reached significance. Because the variants are identical, every "winner" is a false positive.
| Times you peek | False-positive rate (α = 0.05) | False-positive rate (α = 0.01) |
|---|---|---|
| 1 (no peeking) | 5.0% | 1.1% |
| 2 | 8.2% | 1.8% |
| 3 | 10.5% | 2.2% |
| 5 | 13.9% | 3.1% |
| 10 | 19.2% | 4.7% |
| 20 | 24.3% | 6.3% |
| 50 | 32.3% | 8.9% |
10,000 simulated A/A experiments per condition, seeded and reproducible. Peeking 50 times on a 10,000-visitor test means checking roughly every 200 visitors — about what "glancing at the dashboard every day" looks like for a typical two-week test.
A significance level of α = 0.05 means: if you run the test once, there is a 5% chance of a false positive. Each additional look is another chance for noise to cross the threshold, and a stop-at-significance rule keeps every lucky crossing while ignoring the recovery that would have followed.
Note: Bayesian dashboards are not automatically immune — stopping the moment a posterior probability crosses a fixed threshold has an optional-stopping problem of its own.