Power Analysis for Multiple Regression
A Priori Power Analysis for Multiple Regression · Also known as: regression power analysis, sample size estimation regression, f² power analysis, Güç Analizi — Regresyon
Power analysis for multiple regression is a pre-study procedure, formalised by Jacob Cohen (1988), that calculates the minimum sample size needed to detect a regression effect of a given size with adequate statistical power. It uses the anticipated R² (or the equivalent Cohen's f² effect size) and the number of predictors to determine how many observations must be collected before data collection begins.
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When to use it
Use this procedure when planning a multiple regression study with continuous predictors and a continuous outcome, before data collection begins. Two inputs must be specified: the number of predictors (u) and the anticipated effect size expressed as either an expected R² value or Cohen's f². Effect size estimates should be grounded in prior literature, pilot data, or the smallest effect deemed scientifically meaningful — not invented arbitrarily. The method does not assume normality of the outcome and requires only that the F-based omnibus test is the inferential target. If n is already fixed by practical constraints and the goal is to determine achievable power, the same framework is used in post-hoc (sensitivity) mode.
Strengths & limitations
- Prevents both underpowered studies (which miss real effects) and wastefully over-large samples.
- Based on a transparent, formally derived framework with over three decades of validation across disciplines.
- The f² effect size is directly interpretable: small ≈ 0.02, medium ≈ 0.15, large ≈ 0.35 (Cohen, 1988).
- Can be adapted to detect the incremental R² of a subset of predictors, not only the omnibus model effect.
- The result is only as trustworthy as the anticipated effect size; inflated pilot estimates lead to underpowered final studies.
- Covers only the omnibus F test; power for individual regression coefficients requires separate, more complex calculations.
- Does not account for missing data, non-normal residuals, or model misspecification, all of which reduce effective power.
Frequently asked
What value should I use for the expected R²?
Ground it in prior literature on the same or closely related constructs. If no suitable literature exists, Cohen's (1988) benchmarks provide a conservative starting point: a small effect (f² = 0.02, R² ≈ 0.02), medium effect (f² = 0.15, R² ≈ 0.13), and large effect (f² = 0.35, R² ≈ 0.26). When in doubt, plan for a smaller effect than you expect — this builds in a safety margin.
How does the number of predictors affect the required sample size?
Each additional predictor costs one degree of freedom from the residual, making it harder to detect the same effect. For a fixed target power and effect size, adding predictors requires a larger N. This is why including unnecessary predictors inflates sample size requirements and why model parsimony matters at the design stage.
Can I use this for hierarchical regression?
Yes, with an adjustment: focus on the incremental R² contributed by the block of new predictors (ΔR²) rather than the total model R². Convert ΔR² to f² using the same formula (f² = ΔR² / (1 − R²_full)) and use the number of predictors in the new block as u. Cohen (1988) covers this case explicitly.
What should I do if the required N exceeds what is feasible to collect?
First, verify that the effect size estimate is realistic and not conservatively small. If N is truly infeasible, report the power your available sample achieves and acknowledge it as a study limitation. Alternatively, consider simplifying the model by reducing the number of predictors, which lowers the required N for the same target power.
Sources
- Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum Associates. ISBN: 978-0805802832
- Green, S. B. (1991). How Many Subjects Does It Take To Do A Regression Analysis? Multivariate Behavioral Research, 26(3), 499–510. DOI: 10.1207/s15327906mbr2603_7 ↗
How to cite this page
ScholarGate. (2026, June 1). A Priori Power Analysis for Multiple Regression. ScholarGate. https://scholargate.app/en/statistics/power-analysis-regression
Which method?
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