Correlation Power Calculator

Plan correlation studies with flexible statistical controls. Review power curves, thresholds, and scenario comparisons instantly. Make confident design choices before collecting any expensive data.

Calculator Inputs

Reset

Choose a mode to estimate power, required sample size, or the minimum detectable correlation under your preferred significance rules.

Analysis mode

Anticipated correlation (r)

Use a signed value between -0.9999 and 0.9999.

Sample size (n)

Needed for power and detectable effect calculations.

Target power

Common planning target: 0.80 or higher.

Alpha level

Typical values are 0.05 or 0.01.

Tail setting

Alternative direction

Direction matters for one-tailed analysis.

Displayed decimals

Graph upper sample size

Used for sample-size power curves.

Example Data Table

Scenario	Expected r	n	Alpha	Tail test	Approx. Power
Customer sentiment and retention study	0.30	85	0.05	Two-tailed	0.8003
Biomarker and response screening	0.25	120	0.05	Two-tailed	0.7889
Engagement pilot correlation check	0.35	60	0.05	Two-tailed	0.7879

Formula Used

This calculator uses a Fisher z approximation for planning and power estimation in correlation studies. It is practical for design decisions and fast scenario testing.

Fisher transformation: z_r = 0.5 × ln((1 + r) / (1 - r))

Shift parameter: δ = √(n - 3) × z_r

Two-tailed power: 1 − Φ(z_crit − δ) + Φ(−z_crit − δ)

One-tailed power: 1 − Φ(z_crit − δ) for positive alternatives

Critical threshold: |r_crit| ≈ tanh(z_crit / √(n − 3))

Here, Φ denotes the standard normal cumulative distribution function. The method assumes independent observations and a design where Fisher’s z approximation is reasonable for planning.

How to Use This Calculator

Choose the analysis mode that matches your planning question.
Enter the expected correlation from prior studies, expert judgment, or pilot data.
Set the alpha level and choose one-tailed or two-tailed testing.
Enter either sample size or target power, depending on the chosen mode.
Press Calculate to show the result above the form.
Review the summary metric, result table, and the Plotly graph.
Use the CSV or PDF buttons to export the displayed results.

FAQs

1) What does this calculator estimate?

It estimates statistical power for a correlation study, the minimum sample size needed for a target power, or the smallest correlation likely to be detectable with a chosen sample size.

2) Why is Fisher z used here?

Fisher z stabilizes the sampling behavior of correlation coefficients and makes power planning much easier. It is widely used for approximate study design and scenario comparisons.

3) When should I use a one-tailed test?

Use a one-tailed test only when your hypothesis has a justified direction before seeing data. If both positive and negative associations matter, two-tailed testing is safer.

4) What is a good target power?

A target power of 0.80 is common. Higher targets such as 0.90 reduce the chance of missing a real effect, but they usually require larger sample sizes.

5) Can I enter a negative correlation?

Yes. Negative values are supported. For one-tailed settings, direction affects power. For two-tailed settings, the magnitude matters most when assessing detectability.

6) Are the results exact?

No. These are planning approximations based on the Fisher z framework. They are useful for study design, but exact small-sample behavior can differ from the approximation.

7) Why can small samples be risky?

Small samples usually give unstable correlation estimates and weaker power. That can increase false negatives and make effect sizes appear more volatile than expected.

8) How should I choose the expected correlation?

Use prior literature, domain benchmarks, pilot results, or a conservative practical minimum. Overstating the expected effect can produce unrealistically small sample size recommendations.