**A Test of the Equivalence of Two Correlation
Coefficients
{From the Institute of Phonetic Sciences (IFA):
http://www.fon.hum.uva.nl/}**

*Characteristics:*

This is a quite insensitive test to decide whether two correlations have
different strengths. In the
standard tests for correlation, a correlation coefficient is tested against
the hypothesis of *no* correlation, i.e., *R = 0*. It is possible to
test whether the correlation coefficient is *equal to* or *different from*
another fixed value, but this has few uses (when can you make a reasonable guess
about a correlation coefficient?). However, there are situations where you would
like to know whether a certain correlation strength realy is different from
another one.

*H0:*

Both samples of pairs show the same correlation strength, i.e., *R1 = R2*.

*Assumptions:*

The values of both members of both samples of pairs are Normal (bivariate)
distributed.

*Scale:*

Interval (for the raw data).

*Procedure:*

The two correlation coefficients are transformed with the Fisher Z-transform (
Papoulis):

Zf = 1/2 * ln( (1+R) / (1-R) )

The difference

z = (Zf1 - Zf2) / SQRT( 1/(N1-3) + 1/(N2-3) )

is approximately Standard Normal distributed.

If both the correlation coefficient *and* the sample size of one of the
samples are equal to *zero*, the standard procedure for
correlation coefficients is used on the other values.

*Level of Significance:*

Use the z value to determine the level of significance.

*Approximation:*

This is already an approximation which should be used only when both samples (N1
and N2) are larger than 10.

*Remarks:*

Check whether you realy want to know whether the *correlation coefficients*
are different. Only rarely is this a usefull question.

A warning is printed next to the significance level if the number of samples is
too small (i.e., less than 11).

You can compute this test by clicking HERE.