Both samples of pairs show the same correlation strength, i.e., R1 = R2.
The values of both members of both samples of pairs are Normal (bivariate) distributed.
Interval (for the raw data).
The two correlation coefficients are transformed with the Fisher Z-transform ( Papoulis):
Zf = 1/2 * ln( (1+R) / (1-R) )
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.
This is already an approximation which should be used only when both samples (N1 and N2) are larger than 10.
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).