Power Analysis Sample Size Regression Calculator

Calculator

Effect size source

Full model R squared

Reduced model R squared

Direct Cohen f squared

Tested predictors

Total predictors in model

Alpha level

Target power

Current sample size

Minimum candidate sample

Maximum candidate sample

Missing data reserve percent

Formula Used

Whole model effect: f² = R² / (1 − R²)

Incremental effect: f² = (R² full − R² reduced) / (1 − R² full)

Regression F test: df1 = tested predictors, df2 = N − total predictors − 1

Noncentrality: λ = f² × N

Power: Power = 1 − CDF of the noncentral F distribution at the critical F value.

The script searches upward and returns the smallest sample that reaches the selected power.

How to Use This Calculator

Select the effect size source first. Use whole model R squared for a full regression test. Use R squared increase when testing a block of added predictors. Use direct f squared when it comes from a prior study.

Enter the number of tested predictors. Then enter total predictors in the full model. Add alpha, target power, and candidate sample limits. Use the missing data reserve to estimate how many participants should be recruited.

Press Calculate to show results above the form. Use CSV or PDF buttons to save the same result.

Example Data Table

Scenario	Full R²	Reduced R²	Tested Predictors	Total Predictors	Alpha	Power
Small block effect	0.12	0.08	2	6	0.05	80%
Medium whole model	0.18	0.00	4	4	0.05	90%
Strict alpha study	0.20	0.10	3	8	0.01	80%

Regression Power Planning

Regression studies need enough observations to detect useful relationships. A weak plan can miss a real effect. It can also waste time by collecting far more data than needed. Power analysis connects the expected effect, alpha level, predictors, and desired detection chance. This calculator supports whole model tests and incremental predictor block tests. It is useful before surveys, experiments, and observational modeling.

Effect Size Matters

The main input is Cohen's f squared. You may enter it directly. You may also derive it from model R squared. For a block test, compare the full model with the reduced model. A larger f squared means the signal is easier to detect. Small values need larger samples. Large values need fewer records, but they still need clean data.

Predictors And Degrees Of Freedom

Regression power depends on how many predictors are tested. It also depends on the total predictors in the full model. Extra predictors reduce residual degrees of freedom. That usually increases the sample requirement. The tested predictors form the numerator degrees of freedom. The remaining sample information forms the denominator degrees of freedom.

Alpha And Power

Alpha controls false positive risk. Common choices are 0.05, 0.01, and 0.10. Lower alpha values are stricter. They need larger samples. Power is the chance of detecting the target effect when it is real. Many studies use 80 percent power. Critical work may require 90 percent or higher.

Interpreting Results

The recommended analysis sample is the minimum usable sample. The recruitment sample adds a reserve for missing data or dropouts. Use realistic loss percentages. A strong result still needs good measurement, sound assumptions, and meaningful variables. Regression can be sensitive to outliers, collinearity, nonlinearity, and missing values.

Best Practice

Run several scenarios before collecting data. Compare optimistic, expected, and conservative effect sizes. Report the selected alpha, power, predictors, and effect source. This makes the planning method transparent. The tool gives a planning estimate, not a guarantee. Review the design with a statistician when decisions are costly. Also inspect residual plots after fitting the model. Power planning starts the study, but diagnostics protect the final interpretation. Clear coding and consistent measurement make the planned sample more useful during later analysis.

FAQs

What is regression power analysis?

It estimates the sample size needed to detect a regression effect. It uses effect size, alpha, target power, and predictor counts.

What does Cohen f squared mean?

Cohen f squared measures regression effect size. It compares explained variance with unexplained variance. Larger values usually need smaller samples.

When should I use R squared increase?

Use it when testing added predictors after controlling for existing predictors. Enter full and reduced model R squared values.

What is a good target power?

Many studies use 80 percent power. Higher stakes research may use 90 percent or 95 percent power.

Why do total predictors matter?

Total predictors reduce residual degrees of freedom. More predictors usually require more observations for stable regression testing.

What alpha level should I choose?

Alpha 0.05 is common. Use 0.01 for stricter evidence. Use 0.10 only when a more exploratory plan is acceptable.

What is the recruitment sample?

It is the recommended analysis sample increased for missing data or dropout reserve. It helps protect the final usable sample.

Is this result a final guarantee?

No. It is a planning estimate. Data quality, model assumptions, measurement error, and missing values can change real study performance.