Discover how effect size, sample size, and significance threshold jointly determine whether your study can detect a true signal. Tune the parameters and watch the overlapping distributions shift in real time.
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Power Visualization
Effect Size (Cohen's d)
Sample Size per Group
Total participants = n × 2 (two groups). Every power number in this guide is for the two-sample comparison; a one-sample test with the same n has different power, so do not reuse these values for it.
Significance Level (α)
Standard significance threshold: 5% false positive rate
Two-tailed tests are more conservative: they split α across both tails. Use one-tailed only when the direction of effect is known in advance.
Power Analysis Results
0.81
Statistical Power
GoodSignificance (α)
0.05
Type II Error (β)
0.19
Effect Size (d)
0.50 (Medium)
n per group
64
Effect Size Calculator
Cohen's d = |μ₂ − μ₁| / σ
|110 − 100| / 15 = 0.667
Sample Size Planner
Target Power
Effect Size (d)
MediumSignificance Level
Power at varying n (d = 0.50, α = 0.05)
| n per group | Power | β |
|---|---|---|
| 10 | 0.201 | 0.799 |
| 20 | 0.352 | 0.648 |
| 30 | 0.491 | 0.509 |
| 50 | 0.705 | 0.295 |
| 64 | 0.807 | 0.193 |
| 100 | 0.942 | 0.058 |
| 200 | 0.999 | 0.001 |
Type I Error (α)
The probability of rejecting a true null hypothesis: a false positive. You control this directly by choosing α.
Type II Error (β)
The probability of failing to reject a false null hypothesis: a false negative. β = 1 − Power.
Power = 1 − β
The probability of correctly detecting a real effect. Power ≥ 0.80 is the standard convention for confirmatory research.