How this calculation works
Build an approximate confidence interval around an observed Pearson correlation.
THE FORMULA
Bounds=tanh(atanh(r)±z*/√(n−3))A worked example
At r=0 and n=103, z*=1.96 gives bounds close to ±0.194.
Good to know
Assumes independent pairs and uses the Fisher normal approximation.
Reference: OpenStax Introductory Statistics (opens in a new tab) ↗
Read the result
Build an approximate confidence interval around an observed Pearson correlation.
The primary result is labeled “Lower confidence bound”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Assumes independent pairs and uses the Fisher normal approximation.
For a related exercise, try the statistics calculator.
A few questions, answered
How can I check the default inputs by hand?
At r=0 and n=103, z*=1.96 gives bounds close to ±0.194.
Which rule does this calculator apply?
Bounds=tanh(atanh(r)±z*/√(n−3))