Build regression power plans from effect size and predictors. Check sensitivity, power, or sample needs. Use practical outputs for faster statistical planning decisions today.
| Scenario | Alpha | Sample Size | Total Predictors | Tested Predictors | Effect Size f² | Power |
|---|---|---|---|---|---|---|
| Overall model planning | 0.05 | 120 | 6 | 6 | 0.15 | 0.8923 |
| Added predictor block | 0.05 | 150 | 8 | 2 | 0.10 | 0.9297 |
| Stricter alpha design | 0.01 | 200 | 10 | 3 | 0.08 | 0.7832 |
Overall model effect size: f² = R² / (1 - R²)
Added predictor block effect size: f² = ΔR² / (1 - R² full)
Numerator degrees of freedom: u = tested predictors
Denominator degrees of freedom: v = N - p - 1
Noncentrality parameter: λ = f² × (u + v + 1)
Power: 1 - CDF of the noncentral F distribution at the critical F value
Symbols: N is sample size, p is total predictors, and u is the predictor count being tested.
For an overall model test, tested predictors automatically match total predictors. For a predictor block test, tested predictors should be the specific variables in the added block.
Multiple regression power analysis helps you plan a reliable study. It shows whether your design can detect a meaningful effect. This matters before data collection starts. It also matters when you review an existing design. Good planning lowers the risk of weak conclusions.
A power analysis connects five core inputs. These are alpha, sample size, effect size, predictors, and target power. Alpha controls the false positive rate. Sample size controls information depth. Effect size reflects expected signal strength. Predictor counts shape the test degrees of freedom. Target power states how often a real effect should be detected.
This calculator supports two common regression questions. The first tests the overall model against zero explained variance. The second tests an added block of predictors. That second option is useful for hierarchical regression. It helps you judge whether a new variable set adds meaningful value after controls are entered.
Effect size is entered as Cohen’s f². For the full model, f² equals R² divided by one minus R². For an added block, f² equals change in R² divided by one minus the full model R². Small differences in f² can change required sample size. That is why sensitivity analysis is useful.
Use the calculator in three ways. Solve for power when you already know sample size and f². Solve for sample size when you need a planning target. Solve for effect size when you want the minimum detectable effect. This makes the page useful for proposal writing, thesis design, audit studies, and internal analytics planning.
Interpret results with context. A high power estimate does not guarantee a good model. You still need valid measures, reasonable assumptions, and clean data. Use domain knowledge when choosing predictors. Avoid inflating predictor counts without purpose. A simpler model with stronger theory often performs better than a crowded model with weak logic.
Report both the numeric output and the assumptions behind it. Mention the expected effect size source. Cite prior studies, pilot data, or business benchmarks. When results are borderline, compare several scenarios. That gives stakeholders a realistic range. Better scenario planning leads to stronger budgeting, cleaner timelines, and more credible statistical decisions.
Use overall model when you test whether all predictors explain variance together. Use predictor set when you test whether a specific block adds value after other predictors are already in the model.
f² is a standardized effect size for regression. For the full model, use R² divided by one minus R². For a predictor block, use change in R² divided by one minus full-model R².
Total predictors are all independent variables in the final model. Tested predictors are only the variables being evaluated in the F test. For the overall model, both values are the same.
Sample size affects denominator degrees of freedom and the noncentrality parameter. Larger samples usually raise power. Very small samples can make regression tests unstable and harder to interpret.
Alpha is the significance level. Lower alpha reduces false positives, but it also lowers power when other inputs stay fixed. Common choices are 0.05 and 0.01.
Yes. Sensitivity mode solves for the smallest effect size the design can detect at your chosen alpha, sample size, and target power. This is useful for feasibility checks.
No. Power analysis helps with planning, not model validity. You still need good theory, reliable measures, clean data, assumption checks, and sensible predictor selection.
Overall model power focuses on total explained variance. Added-predictor power focuses on incremental variance beyond existing controls. The right option depends on your study question and regression design.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.