Sample size for correlation and regression
When your sample doesn’t come from a population you can count, or your advisor asks you to justify it with statistical power, the calculation starts from the analysis you will run. Choose correlation or regression, enter the effect size you expect and get how many people you need. It gives the same results as G*Power.
Which analysis you will run
Tails
Alpha
Power
Minimum sample size
85
people
By effect size
| Small (r = 0.10) | 783 |
| Medium (r = 0.30) | 85 |
| Large (r = 0.50) | 30 |
How to report it
Sample size was determined with an a priori power analysis for a Pearson correlation (two-tailed test), with an expected effect size of r = .30, α = .05 and power of .80. A minimum sample of 85 participants is required.
The calculation runs in your browser. We don’t store what you type.
How it’s calculated
Correlation: Fisher’s z transformation is used. n = [(z of alpha + z of power) / C]² + 3, where C = ½ × ln[(1 + r) / (1 − r)].
Multiple linear regression: F test of R² greater than zero, with the noncentral F distribution and λ = f² × N, like G*Power ("Linear multiple regression: Fixed model, R² deviation from zero").
The regression effect size is f² = R² / (1 − R²). Cohen (1988) suggests 0.02 small, 0.15 medium and 0.35 large.
The smallest N that reaches the power you chose is returned.
How to read the result
- The most common setting in theses is alpha = 0.05 and power = 0.80: an 80% chance of detecting the effect if it exists.
- For correlation, Cohen suggests r = 0.10 small, 0.30 medium and 0.50 large. Without prior evidence, 0.30 is the usual reference.
- If previous studies used your variables, use the effect they found: it is the strongest justification.
- Add a margin for incomplete or discarded responses, for example 10% to 20% more.
Frequently asked questions
- Does it match G*Power?
- Yes. For regression it uses the same noncentral F as G*Power. For example, f² = 0.15, 5 predictors, alpha 0.05 and power 0.80 give N = 92, the same as G*Power. For correlation it uses Fisher’s approximation, which can differ by 1 or 2 people from G*Power’s exact option.
- What effect size should I use?
- Ideally the one from earlier studies with the same variables. If there are none, use Cohen’s medium effect (r = 0.30 or f² = 0.15) and say so in your method section.
- What if my population is small and countable?
- Then use the population sample size calculator, with margin of error and confidence level.
- One-tailed or two-tailed?
- Two-tailed, unless your hypothesis states the direction of the relationship (for example, "more stress, lower performance") and your advisor accepts one tail.
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