Significance of the Difference between Two Correlations Formulas

Significance of the Difference between Two Correlations Formulas

Below you will find descriptions and details for the 3 formulas that are used to compute probability values (p-values) for the difference between two correlation coefficients.

Cumulative distribution function (CDF) for the standard normal distribution:

Variable definitions:
erf = error function

Error function:

Standard score (z-value) for the difference between two correlations:

Variable definitions:
r₁ and r₂ = the correlation coefficients for the two samples
n₁ and n₂ = the sample sizes associated with the two correlation values