Advanced planning inputs
Configure the Regression Test
Use total predictors for the full model. Tested predictors are the variables or block examined by the F test.
Example data table
Example Planning Inputs
| Total N | Tested predictors | Total predictors | Cohen f² | Alpha | Planning use |
|---|---|---|---|---|---|
| 80 | 1 | 3 | 0.15 | 0.05 | Single added predictor |
| 120 | 2 | 4 | 0.15 | 0.05 | Two-predictor block |
| 220 | 4 | 7 | 0.08 | 0.01 | Conservative precision study |
Formula used
Regression F-Test Relationships
The calculator applies a fixed-model multiple-regression F test. It tests whether a selected predictor block improves the full model beyond the reduced model.
Here, u is the tested predictor count, p is the total predictor count, N is total sample size, and FNCF is the noncentral F cumulative distribution.
How to use this calculator
Plan a Regression Study
- Select the calculation mode that matches your planning question.
- Enter the number of predictors tested by the F test.
- Enter every predictor contained in the full regression model.
- Use Cohen f² directly, or enter full and reduced R² values.
- Set alpha and, when needed, a target power such as 0.80.
- Calculate the result, inspect degrees of freedom, and copy the displayed R command for validation.
Study design guidance
Using Power Estimates in Physics Research
Multivariate regression is common in physics. Researchers use it when several predictors explain one measured response. Examples include temperature, field strength, detector calibration, and exposure time. A regression model can isolate relationships. It can also control nuisance variables. However, a fitted model is not trustworthy. A small sample may hide a pattern. A large sample may detect a pattern. Power analysis helps choose a study size before measurements begin.
Regression power is the probability of detecting an effect. Calculator uses an F test for a tested predictor set. The set may contain several predictors. Other predictors can remain as controls. The model compares a reduced equation against a full equation. Cohen’s f² is the key quantity. It expresses the gain in explained variance after adding tested predictors. Larger f² values and more observations produce higher power. More predictors reduce residual degrees of freedom.
Use the full-model R² and reduced-model R² when available. Their difference is the incremental variance explained by tested predictors. Convert that difference into f² by dividing it by one minus the full-model R². This makes the effect size compatible with the F distribution. You may instead enter a planned f² directly. A small f² can represent a subtle physical relationship. An f² can represent a measurable response. Choose values from pilot data, published work, simulation, or a scientifically meaningful effect.
The calculator uses tested predictors and total predictors separately. This matters when covariates appear. The numerator degrees of freedom equal the tested predictor count. The denominator degrees of freedom equal sample size minus total predictors minus one. The noncentrality parameter combines effect size with usable sample information. The program finds the critical F value at the alpha level. It estimates power from the noncentral F distribution. This approach suits fixed-model regression comparisons.
Choose Calculate Power when your sample size is fixed. Choose Required Sample Size when desired power is known. Choose Minimum Detectable Effect when sample size cannot change. Review practical limits. Recruitment, instrument time, budget, and missing data can change usable sample. Add a reasonable allowance for exclusions. Do not count repeated measures as independent unless the model supports that assumption.
Interpret output as a planning estimate. It relies on linear-model assumptions. Residuals should be independent. Variance should be stable across fitted values. Measurements should be reliable. Severe multicollinearity can make coefficients unstable. Model misspecification can reduce practical value. Power analysis cannot repair weak design choices. It quantifies sample requirements after the hypothesis and model are clearly specified.
R users can reproduce the central setup with a multiple-regression F-test function. The displayed command uses tested and residual degrees of freedom, f², and alpha. Compare the estimate with simulation when the design is unusual. Simulations help with interactions, missingness, clustered observations, nonlinear terms, or constrained predictors. Document selected inputs in a laboratory protocol. That record aids future audits. Good planning improves conclusions, resources, transparency, and scientific confidence.
Frequently asked questions
Regression Power Questions
1. What does Cohen f² measure?
Cohen f² measures the added explained variance from tested predictors relative to unexplained variance in the full model. It is useful for planning an incremental regression F test.
2. Why enter total predictors separately?
Total predictors determine residual degrees of freedom. Controls consume model information even when they are not part of the tested predictor block.
3. Should I enter adjusted R² values?
No. Use ordinary model R² values for the effect-size conversion. Adjusted R² includes a predictor penalty and does not match this standard f² relationship.
4. Does this calculator test individual coefficients?
It estimates power for an F test of one or more predictors as a block. A coefficient-specific t-test needs a different calculation and correlation structure.
5. Which alpha level should I use?
Use the threshold stated in your protocol. A value of 0.05 is common. More stringent thresholds need more evidence and can increase required sample size.
6. Is 80% power always enough?
Not always. Eighty percent is a common minimum. Higher-stakes experiments may justify 90% or more, especially when repeating the study would be difficult.
7. What happens when residual degrees of freedom are low?
Critical F values become less favorable and estimates become less stable. Increase sample size or simplify the model when too many predictors compete for limited data.
8. Is the numerical result exact?
The calculator uses numerical evaluation of the noncentral F distribution. It is a planning estimate. Compare unusual designs with a dedicated simulation in R.
9. Does the result include missing-data losses?
No. Enter the intended analyzable sample. Add a justified allowance for attrition, excluded observations, instrument failures, or incomplete predictor measurements before recruitment.
10. Can I reproduce this calculation in R?
Yes. The result panel provides a pwr package command. It uses the numerator and residual degrees of freedom with f² and alpha.
11. When should I use simulation instead?
Use simulation for interactions, nonlinear models, correlated residuals, clusters, repeated measures, unequal variances, missingness patterns, or complex sampling constraints.