Calculator Inputs
Example Data Table
| Scenario | N | p | u | Alpha | f² | Partial R² | Power |
|---|---|---|---|---|---|---|---|
| Scenario A | 70 | 4 | 4 | 0.05 | 0.0800 | 0.0741 | 0.0177 |
| Scenario B | 120 | 5 | 3 | 0.05 | 0.1500 | 0.1304 | 0.0010 |
| Scenario C | 180 | 6 | 6 | 0.01 | 0.2000 | 0.1667 | 0.0000 |
| Scenario D | 250 | 8 | 2 | 0.05 | 0.0300 | 0.0291 | 0.0052 |
Formula Used
The calculator evaluates power for the F test in fixed multiple regression. It supports the full model test and the extra sum of squares test for a predictor block.
- Effect size: f² = R² / (1 − R²)
- Numerator degrees of freedom: df1 = u
- Denominator degrees of freedom: df2 = N − p − 1
- Critical value: Fcrit = F−1(1 − α; df1, df2)
- Noncentrality: λ = f² × (u + df2 + 1)
- Power: 1 − CDF of the noncentral F distribution at Fcrit
If you enter expected partial R², the calculator converts it to Cohen’s f² before computing the noncentral F statistic.
How to Use This Calculator
- Choose the analysis mode that matches your planning question.
- Enter the total number of predictors in the full model.
- Enter how many predictors are being tested in the focal block.
- Provide sample size when solving power, effect size, or alpha.
- Provide alpha unless you want the tool to solve alpha.
- Enter target power when solving sample size, effect size, or alpha.
- Pick Cohen’s f² or expected partial R² as the effect metric.
- Click Calculate to display the result above the form.
- Use the CSV or PDF buttons to export the result table.
Multiple Regression Power Analysis Guide
Why power analysis matters
Multiple regression power analysis helps you decide whether a planned study can detect the effect you care about. It protects your design from being too small, too expensive, or too weak for the research question. A study with low power may miss meaningful predictor effects even when they exist. A study with strong power supports clearer decisions before data collection starts.
What the inputs mean
The calculator uses four main planning pieces. Sample size tells the model how many observations are available. The total number of predictors defines model complexity. The tested predictor count identifies the block being evaluated. Alpha sets the decision threshold for statistical significance. Effect size captures the strength of the tested predictor set. You can enter this strength as Cohen’s f² or as expected partial R².
How to interpret the result
Power is the probability of detecting the chosen effect under the stated assumptions. Many researchers target 0.80, but stronger designs may target 0.90 or higher. The calculator also reports degrees of freedom, the critical F value, noncentrality, and the partial R² implied by the effect size. These values help you document the assumptions behind your design choices.
Planning better regression studies
Good regression planning links theory, variables, and sample size. If you expect a small incremental effect for a predictor block, you usually need a larger sample. If your model includes many predictors, denominator degrees of freedom shrink, so power can fall quickly. That is why power analysis should happen before collecting data, not after results are already known. This tool gives a practical way to compare designs, test alternative assumptions, and justify a realistic sample target for your study.
FAQs
1. What does Cohen’s f² represent?
Cohen’s f² measures effect size for the tested regression block. Larger values indicate stronger explanatory contribution relative to unexplained variance.
2. What is partial R² here?
Partial R² is the proportion of remaining outcome variance explained by the tested predictor set after accounting for other predictors already in the model.
3. When should I set u equal to p?
Use u equal to p when you want power for the overall regression model against the null model with no predictors.
4. Can I test only a subset of predictors?
Yes. Set p to the full model size and set u to the number of focal predictors being tested as one block.
5. Why does adding predictors reduce power sometimes?
More predictors reduce denominator degrees of freedom. If the added predictors do not increase effect size enough, power can decline.
6. What target power should I choose?
Many studies use 0.80. Higher targets such as 0.90 are helpful when missing a real effect would be costly.
7. Does this calculator assume a fixed model?
Yes. It uses the standard fixed multiple regression F test with a noncentral F distribution for power estimation.
8. Should I enter observed R² from a finished study?
Planning works best with expected effect sizes from prior evidence, theory, pilot data, or domain expertise rather than post hoc observed estimates.