# 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.

### Can you compare two correlation coefficients?

Yes, indeed. 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:

$H_0: \rho_1 = \rho_2$ $H_a: \rho_1 \ne \rho_2$

You will reject the null hypothesis when there is enough evidence to claim that the sample correlations come from population with different population correlations.

### Z-test for comparing correlation coefficients

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

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

where

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

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.