Correlation Confidence Interval
Estimate a Pearson correlation interval with Fisher’s z transform.
Your numbers
Lower correlation bound
Approximation assumes independent paired observations and approximately bivariate-normal data.
Scenario comparison
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Formula
Use tanh[atanh(r)±z/√(n−3)]. r is sample Pearson correlation, n is paired observation count, and z is the two-sided standard-normal critical value for the chosen confidence. The transforms convert between correlation and Fisher's scale.
Estimate a Pearson correlation interval with Fisher’s z transform.
Worked example
- Sample correlation r
- 0
- Paired observations
- 30
- Confidence level (%)
- 95
- Lower correlation bound
- -0.360269222596
- Upper correlation bound
- 0.360269222596
Scope and limitations
Approximation assumes independent paired observations and approximately bivariate-normal data.
Inputs are checked for missing values and allowed ranges. A result outside the finite numeric range is not displayed. Rounding affects display, while the calculation uses the model’s numeric precision.
Check your units and assumptions before relying on a result. Changing a label does not convert a currency or physical unit.
Formula version: 298fb2aab2da · Example checked: