Depending upon the input, one of four different tests of correlations is done.
1) For a sample size n, find the t value for a single correlation where $$t = \frac{r * \sqrt(n-2)}{\sqrt(1-r^2)}
$$ and
$$se = \sqrt{\frac{1-r^2}{n-2}}) $$.
2) For sample sizes of n and n2 (n2 = n if not specified) find the z of the difference between the z transformed correlations divided by the standard error of the difference of two z scores:
$$z = \frac{z_1 - z_2}{\sqrt{\frac{1}{(n_1 - 3) + (n_2 - 3)}}}$$.
3) For sample size n, and correlations r12, r13 and r23 test for the difference of two dependent correlations (r12 vs r13).
4) For sample size n, test for the difference between two dependent correlations involving different variables.
For clarity, correlations may be specified by value. If specified by location and if doing the test of dependent correlations, if three correlations are specified, they are assumed to be in the order r12, r13, r23. Consider the example the example from Steiger:
where Masculinity at time 1 (M1) correlates with Verbal Ability .5 (r12), femininity at time 1 (F1) correlates with Verbal ability r13 =.4, and M1 correlates with F1 (r23= .1). Then, given the correlations: r12 = .4, r13 = .5, and r23 = .1, t = -.89 for n =103, i.e.,
r.test(n=103, r12=.4, r13=.5,r23=.1)