Calculator Inputs
Use direct f² or derive f² from reduced and full model R².
Power Curve
This Plotly graph shows how projected power changes as sample size moves around your current planning range.
Example Data Table
These example rows use the active assumptions shown on the page, so the table updates naturally with your submitted settings.
| Sample Size | Alpha | Total Predictors | Tested Predictors | Effect Size f² | Projected Power |
|---|---|---|---|---|---|
| 60 | 0.050 | 6 | 2 | 0.1500 | 0.7453 |
| 90 | 0.050 | 6 | 2 | 0.1500 | 0.9084 |
| 120 | 0.050 | 6 | 2 | 0.1500 | 0.9710 |
| 150 | 0.050 | 6 | 2 | 0.1500 | 0.9916 |
| 180 | 0.050 | 6 | 2 | 0.1500 | 0.9978 |
Formula Used
1. If you enter R² values, the calculator derives:
f² = (R²full − R²reduced) / (1 − R²full)
2. The noncentrality parameter is:
λ = f² × n
3. Degrees of freedom are:
df1 = tested predictors, df2 = n − total predictors − 1
4. Critical F comes from the upper tail of the central F distribution at alpha.
5. Power is computed as 1 − CDF of the noncentral F distribution at the critical F threshold.
This implementation is intended for planning and comparison. It assumes a standard fixed-model regression F test framework.
How to Use This Calculator
- Enter a study label so exported files stay identifiable.
- Set sample size, alpha, total predictors, and tested predictors.
- Choose whether to enter f² directly or derive it from R² values.
- Set a target power such as 0.80 or 0.90.
- Click Calculate Power to place the result section above the form.
- Review achieved power, critical F, sensitivity f², and recommended sample size.
- Use the Plotly chart to compare nearby sample-size scenarios.
- Download CSV or PDF if you want to save the planning output.
Frequently Asked Questions
1. What does regression power mean?
Regression power is the probability of detecting a real effect when it truly exists. Higher power lowers the risk of missing meaningful predictors in your model.
2. What is a good target power?
Many studies target 0.80. Stricter research plans may prefer 0.90, especially when missed effects would be costly or difficult to replicate later.
3. Why do I need total predictors and tested predictors?
Total predictors affect denominator degrees of freedom. Tested predictors define the numerator degrees of freedom for the regression F test you want to evaluate.
4. When should I use direct f²?
Use direct f² when previous studies, pilot data, or your statistical plan already provide a Cohen-style effect size estimate for the regression test.
5. When should I derive f² from R² values?
Use R² values when comparing a reduced model against a fuller model. The calculator converts that incremental explained variance into f² automatically.
6. What does the sensitivity f² result show?
Sensitivity f² is the smallest effect size that would reach your chosen target power under the current sample size, predictor count, and alpha level.
7. Why can recommended sample size differ a lot?
Small expected effects need much larger samples. More predictors also reduce degrees of freedom, which can increase the sample requirement noticeably.
8. Is this calculator suitable for final publication decisions?
It is excellent for planning and scenario comparison. For regulated or highly technical studies, confirm assumptions with a statistician and your protocol requirements.