Running a study with n=20 and hoping to detect r=0.3? You have less than a one-in-three chance of finding it. Know the right number before you start.
To detect a moderate correlation around r = 0.30 with 80% power at alpha = 0.05, plan for about 85 participants in a two-tailed study.
To detect r = 0.300 with 80% power at alpha = 0.05 (two-tailed), you need at least 85 participants.
At n = 85, the achieved power is 80.0%. Recruit more than this if you expect exclusions or missing data.
The curve uses your expected r = 0.300.
Add a recruitment buffer for missing data, exclusions, and dropouts. A practical target is about n = 98.
Challenging but achievable. Most labs should plan multiple recruitment waves.
Very feasible. A well-screened online survey can usually reach this range.
Plan carefully. Patient recruitment can take months for this sample size.
Small changes in expected r or power can change recruitment by hundreds of people. Use this table to test whether your design is realistic.
| Expected r | alpha = 0.05, power = 0.80 | alpha = 0.05, power = 0.90 | alpha = 0.01, power = 0.80 |
|---|---|---|---|
| r = 0.10very weak | n = 783 | n = 1,047 | n = 1,164 |
| r = 0.20weak | n = 194 | n = 259 | n = 288 |
| r = 0.30moderate | n = 85 | n = 113 | n = 125 |
| r = 0.50strong | n = 30 | n = 38 | n = 42 |
| r = 0.70very strong | n = 14 | n = 17 | n = 19 |
Correlation power analysis is not a black box. You are deciding four numbers: how large an effect you expect, how much false-positive risk you accept, how much power you want, and how many people you are able to recruit.
This is the most important number. Base it on prior literature in your field, not on a guess that merely feels comfortable.
Cohen's old benchmarks: r = 0.10 small, 0.30 medium, 0.50 large.
Interpret r value →Alpha is the chance you accept for a false alarm when there is really no relationship. Most studies use 0.05.
Use 0.01 when the decision is high-stakes or you have many comparisons.
See the p-value guide →Power is the chance of detecting a real relationship if it actually exists. The usual planning target is 0.80.
If the study matters a lot, 0.90 is a safer target.
Why power matters →More participants do not just make results stronger. They make modest correlations detectable at all.
Small studies can still work, but only for stronger effects.
Understand Pearson r →Correlation coefficients cannot be plugged directly into power formulas because their sampling distribution is skewed. Fisher's z-transformation makes the planning math approximately normal.
Use prior studies or a conservative literature-based estimate.
Most planning uses alpha = 0.05 and power = 0.80.
The z scale behaves much better than raw correlations for planning.
If the formula gives 84.93, recruit 85 and then add a buffer.
Example: with r = 0.30, alpha = 0.05, and 80% power, the calculation lands at about n = 85.
These are planning estimates for a two-tailed test with alpha = 0.05 and 80% power. Stronger expected correlations need fewer participants. Weaker effects need many more.
| Scenario | Expected r | Approx. n | Why it matters |
|---|---|---|---|
| Psychology scale validation | 0.35 | 62 | Typical self-report and validation work |
| Biomedical biomarker association | 0.50 | 30 | Stronger clinical relationships |
| Education research | 0.25 | 124 | Common academic and classroom correlations |
| Economics variables | 0.15 | 347 | Usually weak-to-small effects |
| Genetic association | 0.08 | 1,225 | Very small but sometimes real effects |
| Exploratory study | 0.30 | 85 | A conservative planning value |
Rule of thumb: never plan a correlation study on fewer than 30 people unless the expected effect is very large.
Power analysis is a planning tool. If you already have the data, checking power after the fact does not rescue a weak result.
r = 0.30 is a placeholder, not a law. Real studies in your field may need a very different expected effect size.
If you run many correlations, Bonferroni or a similar correction lowers alpha and raises the sample size you need.
With a large enough n, tiny correlations can become significant while still explaining almost no variance.
Add a buffer of about 10% to 20% so dropouts, exclusions, and bad rows do not undercut your design.
There is no universal minimum, but n = 30 is often treated as a rough floor. For r around 0.30 with 80% power at alpha = 0.05, you need about 85 participants.
By Cohen's conventions, r = 0.10 is small, r = 0.30 is medium, and r = 0.50 is large. Treat those as starting points, not final truth.
Yes, as a planning approximation. The same Fisher z framework is commonly used when planning rank-based correlation studies.
Pilot correlations are often inflated. A conservative shrinkage estimate is safer than planning the main study around the raw pilot result.
Two-tailed is the default. Use one-tailed only when your direction was fixed in advance and reversing direction would not count as success.
Planning sample size is the first step. After that, calculate the actual correlation, test significance, and interpret the effect size before writing the methods section.