CALCULATE WITH CONFIDENCE

Statistics · Sampling & confidence

Confidence Interval for a Correlation Calculator

Calculate a Fisher-z confidence interval for a Pearson correlation from paired data.

Statistics · Sampling & confidence

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Private in-browser calculation · explicit assumptions
A confidence interval pairs a point estimate with model-based uncertainty. Repeated samples produce different intervals.
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
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Statistics result

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Understand sampling uncertainty

How confidence intervals express uncertainty

Confidence Interval for a Correlation. A confidence procedure adds model-based uncertainty around an estimate. Wider confidence levels and noisier or smaller samples generally produce wider intervals.

Method used

atanh(r)±z*/√(n−3), transformed back with tanh.

Wide bounds show that an apparently substantial sample correlation may still be imprecisely estimated.

What the result cannot establish

A 95% confidence interval does not mean there is a 95% probability that a fixed parameter lies inside this realized interval. The 95% describes long-run coverage of the procedure under its assumptions.

Assumption: Classical Fisher-z coverage assumes independent bivariate observations and is sensitive to nonlinearity and influential values.

Quick guide

How to use this calculator

  1. Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
  2. Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
  3. Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.

Calculation method

How the confidence interval for a correlation calculator works

atanh(r)±z*/√(n−3), transformed back with tanh.

Wide bounds show that an apparently substantial sample correlation may still be imprecisely estimated.

Worked example

Confidence Interval for a Correlation example

A sample correlation of 0.5 across 30 pairs produces an asymmetric interval on the correlation scale.

atanh(r)±z*/√(n−3), transformed back with tanh.

Supported inputs

Precision and limits

Model and design

Classical Fisher-z coverage assumes independent bivariate observations and is sensitive to nonlinearity and influential values.

Numerical scope

Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.

Interpretation

Wide bounds show that an apparently substantial sample correlation may still be imprecisely estimated.

Decision boundary

The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.

Privacy

Entered values and calculated results stay in this browser and are not sent to an analytics service.

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