CI for Correlation (Fisher z Transform)
Computes the confidence interval for a correlation coefficient using the Fisher z transformation. The sampling distribution of r is skewed, especially near −1 or +1, which prevents applying the usual symmetric margin. Fisher solved this with a transformation that makes the distribution approximately normal; you build the interval on that scale and then map back to r. The result is an asymmetric interval, narrower on the side near the extremes. Enter the coefficient r and the sample size.
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CI for Correlation (Fisher z Transform)
Computes the confidence interval for a correlation coefficient using the Fisher z transformation. The sampling distribution of r is skewed, especially near −1 or +1, which prevents applying the usual symmetric margin. Fisher solved this with a transformation that makes the distribution approximately normal; you build the interval on that scale and then map back to r. The result is an asymmetric interval, narrower on the side near the extremes. Enter the coefficient r and the sample size.
A confidence band for the coefficient r
Reporting a correlation coefficient as a bare number hides the uncertainty behind it. Like any sample estimate, r has a margin of error, and a confidence interval makes it explicit. The catch is that r's distribution is skewed, which prevents using the usual symmetric margin, especially when the correlation is strong.
The solution came from Fisher, with an ingenious transformation. Applying the inverse hyperbolic tangent to r makes its distribution approximately normal, with a standard error that depends only on the sample size. You build the interval on that well-behaved scale and, at the end, undo the transformation to return to the coefficient's original scale.
Enter the correlation coefficient and the sample size. The tool returns the bounds of the confidence interval for the population r. Note that it's asymmetric: the side facing the extremes, near minus one or plus one, is more compressed — exactly the behavior the Fisher transformation captures and the naive symmetric margin would get wrong.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.