Calculator to Compare Sample Correlations

Instructions: This calculator will conduct a statistical test to compare two given sample correlations \(r_1\) and \(r_2\) by using a Z-test. Please provide the sample correlations and sample size, along with the significance level, and the step-by-steps results of the z-test will be displayed for you:

\(r_1\) =
\(r_2\) =
Sample Size (\(n_1\)) =
Sample Size (\(n_2\)) =
Significance Level (\(\alpha\)) =

Comparing two Correlation Coefficients

More about this z-test for comparing two sample correlation coefficients so you can better use the results delivered by this solver: A z-test for comparing sample correlation coefficients allow you to assess whether or not a significant difference between the two sample correlation coefficients \(r_1\) and \(r_2\) exists, or in other words, that the sample correlation correspond to population correlation coefficients \(\rho_1\) \(\rho_2\) that are different from each other.

The null and alternative hypotheses to be tested in this case are:

\[H_0: \rho_1 = \rho_2\] \[H_a: \rho_1 \ne \rho_2\]

The formula for a z-statistic for two population means is:

\[z = \frac{z_1 - z_2}{\sqrt{\frac{1}{n_1-3} +\frac{1}{n_2-3} }} \]


\[z_1 = \frac{1}{2} \ln\left(\frac{1+r_1}{1-r_1}\right)\] \[z_2 = \frac{1}{2} \ln\left(\frac{1+r_2}{1-r_2}\right)\]

The null hypothesis is rejected when the z-statistic lies on the rejection region, which is determined by the significance level (\(\alpha\)) and the type of tail (two-tailed, left-tailed or right-tailed). You can also use our correlation coefficient calculator if you have sample data and you want to compute the actual correlation coefficients.

In case you have any suggestion, or if you would like to report a broken solver/calculator, please do not hesitate to contact us.

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