Pearson r — Confidence Intervals

This tool reports a two-sided (1−α) confidence interval for a sample correlation r. The top interval is computed by numerically inverting the sampling distribution of R while fixing the population correlation at the observed value (plug-in ρ = r). Concretely, it finds the equal-tailed quantiles x that solve F_R(x; N, ρ = r) = α/2 and 1−α/2 using Gauss–Legendre quadrature. The smaller panel shows the familiar Fisher z large-sample approximation for comparison.

Citation: De Winter, J. C. F. (2025). Pearson r — confidence intervals [Web application]. https://joostdewinter.github.io/pearson-r-ci/

Sample correlation r (−1 < r < 1)

Sample size N (N > 2)

Confidence level (%)

Lower

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Upper

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Method

Sampling distribution

Equal-tailed CI by solving F_R(x; N, ρ=r) = α/2 and 1−α/2.

Lower

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Upper

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Method

Fisher z (approx.)

Large-sample approximation via Fisher’s z transform.