*Example:*

**p <= 0.00216**

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

*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).

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