What this calculator does
This tool estimates achieved power or required sample size for a fixed linear regression test. It supports Cohen’s f² or partial R² input, alpha control, multiple predictors, and a power curve.
Calculator inputs
Power curve
The curve shows how estimated power changes as total sample size rises while alpha, effect size, and predictor counts remain fixed.
Example data table
| Scenario | Sample size | Tested predictors | Total predictors | Alpha | f² | Estimated power |
|---|---|---|---|---|---|---|
| Pilot screening model | 80 | 1 | 4 | 0.05 | 0.02 | 0.0269 |
| Typical applied study | 120 | 2 | 6 | 0.05 | 0.15 | 0.0003 |
| High-signal benchmark | 90 | 2 | 5 | 0.01 | 0.35 | 0.0000 |
Formula used
For fixed linear regression tests:
1. Convert effect size when needed:
f² = partial R² / (1 - partial R²)
2. Define degrees of freedom:
df1 = u
df2 = N - p - 1
Here, u is the number of tested predictors, p is total predictors, and N is sample size.
3. Compute the noncentrality parameter:
λ = f² × N
4. Find the critical F value from the central F distribution:
P(F > Fcritical | H0) = α
5. Compute power from the noncentral F distribution:
Power = P(F > Fcritical | H1)
How to use this calculator
- Select whether you want achieved power or required sample size.
- Choose an effect metric: Cohen’s f² or partial R².
- Enter your alpha level, predictor counts, and effect size.
- Enter sample size for achieved power mode, or target power for planning mode.
- Press calculate to view the summary, interpretation, and power curve.
Practical notes
- This tool is designed for fixed linear regression F tests.
- Tested predictors should never exceed total predictors.
- Denominator degrees of freedom must stay positive.
- For planning, many analysts target at least 0.80 power.
- Cohen’s common f² anchors are 0.02, 0.15, and 0.35.
FAQs
1. What does regression power mean?
Regression power is the chance your test detects a real effect. Higher power means a lower risk of missing meaningful predictor relationships in the population.
2. What is Cohen’s f²?
Cohen’s f² is a standardized effect size for regression. It represents how much explained variance exists relative to unexplained variance.
3. Why do tested predictors and total predictors differ?
Tested predictors are the block being evaluated. Total predictors include every predictor in the full model, including controls and covariates.
4. Can I enter partial R² instead of f²?
Yes. The calculator converts partial R² to Cohen’s f² automatically using f² = partial R² / (1 - partial R²).
5. What power target is usually acceptable?
A common planning target is 0.80. More demanding studies sometimes aim for 0.90 or higher, especially when missing effects would be costly.
6. Why is my required sample size so large?
Required size rises when effects are small, alpha is strict, or the model contains many predictors. Small expected effects often need much larger samples.
7. Does this tool handle logistic regression?
No. This page is for fixed linear regression F tests. Logistic, survival, and multilevel models need different power methods.
8. Should I rely only on the graph?
No. Use the graph for intuition, then confirm decisions with the numeric summary, study design assumptions, and your field’s expected effect sizes.