🔋 Statistical Power Calculator
Estimate the power of a two-sample, two-sided mean comparison using a normal approximation.
📊 Statistics📐 Formula included🧠 Practice questions✓ Free
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Formula and Explanation
Estimate the power of a two-sample, two-sided mean comparison using a normal approximation.
| Concept | Formula or rule |
|---|---|
| Statistical Power Calculator | Power ≈ P(|Z+δ| > zα/2), where δ = d√(n/2) |
How to Use This Calculator
- Enter the sample, counts, probabilities, or summary statistics requested above.
- Keep paired lists in the same order and separate values with commas.
- Select the correct test direction or sample/population option when available.
- Press Calculate and interpret the result together with the supporting statistics.
Worked Example
Example: For d=0.5, n=64 per group, and α=0.05, power is approximately 80%.
✓ Larger effect size or sample size increases power.
Where This Is Used
School & coursework
Check homework, understand formulas, and verify step-by-step statistics exercises.
Research
Explore estimates, uncertainty, distributions, and relationships before using full statistical software.
Business & data analysis
Summarize variation, compare groups, and communicate data-driven findings clearly.
Common Mistakes to Avoid
⚠️
Treating approximate power as exact
Design details and the final test can change power.
Design details and the final test can change power.
⚠️
Choosing effect size after seeing data
Power planning should use a scientifically meaningful effect.
Power planning should use a scientifically meaningful effect.
⚠️
Using power to validate a null result after the fact
Post-hoc power adds little beyond the confidence interval and effect estimate.
Post-hoc power adds little beyond the confidence interval and effect estimate.
Practice Questions
1. What is β when power is 0.8?
Answer: 0.2
2. Does larger n increase power?
Answer: Yes.
3. Does a smaller α usually increase or decrease power?
Answer: Decrease.
Frequently Asked Questions
What is power?▾
The probability of rejecting the null when the specified alternative is true.
What target is common?▾
80% or 90%, depending on context.
What is Type II error?▾
β = 1 − power.