MedCalc  # Comparison of correlation coefficients

 Command: Tests Comparison of correlation coefficients

## Description

Calculates the statistical significance of the difference between two independent correlation coefficients.

This test is not performed on data in the spreadsheet, but on statistics you enter in a dialog box.

## Required input

In the dialog box enter the correlation coefficients and the corresponding number of cases. Next click Test to calculate the statistical significance of the difference between the two correlation coefficients. ## Results

When the P-value is less than 0.05, the conclusion is that the two coefficients are significantly different.

In the example a correlation coefficient of 0.86 (sample size = 42) is compared with a correlation coefficient of 0.62 (sample size = 42). The resulting z-statistic is 2.5097, which is associated with a P-value of 0.0121. Since this P-value is less than 0.05, it is concluded that the two correlation coefficients differ significantly.

In the Comment input field you can enter a comment or conclusion that will be included on the printed report.

## Computational details

The test used by MedCalc is a z-test on Fisher z-transformed correlation coefficients (Hinkel et al, 1988).

• In a first step, the correlation coefficients r are transformed using Fisher z transformation:
$$z_r = {1 \over 2}\ln\left({1+r \over 1-r}\right)$$
• The standard error of the difference is:
$$se_{z_{r_1} - z_{r_2}} = \sqrt { \frac {1}{n1-3} + \frac{1}{n2-3} }$$
• The test statistic z is given by:
$$z = \frac {z_{r_1} - z_{r_2}}{se_{z_{r_1} - z_{r_2}}}$$
For critical values of z, see Values of the Normal distribution.

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