Quick guide
How to use this calculator
- Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
- Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
- 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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