Power LabStatLens

Run a study over and over and watch how often it is discernible. The fraction that reject H₀ is the power — and it converges to the theoretical value as you run more studies. Set the effect size to 0 to watch the false-positive rate settle near α.

Effect size (δ = μ₁ − μ₀) Std. deviation (σ) Sample size (n) Discernibility level (α)
Test:

See the matching theory curves in the Power & Error Visualizer →

Studies

Dance of the p-values

The 30 most recent studies. Each dot is one study's p-value; the dashed line is α. Points below the line reach significance — notice how wildly p bounces even when nothing about the setup changed.

Set the parameters and click +100 to run studies.

Power Lab — Help

This simulates a known-σ one-sample z-test (H₀: μ = 0 vs H₁: μ = δ), the same model as the Power & Error Visualizer. Each study draws n observations, runs the test, and is tallied. The empirical reject-rate converges to the analytic power shown beside it. Set δ = 0 to see the Type I error rate (≈ α).

A note on wording: α is the discernibility level here, following the course text. Many books and exercise sets call the same number the significance level — they mean the same thing.

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+1 study
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+100 studies
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New to this? Start with the plainer Decision Errors page.