r_{1}- r_{2} (
r_{engineers} - r_{humanities} in this example)
and
the value specified by the null hypothesis (zero) as large or larger
than the difference observed in the experiment. Since the sampling
distribution of Pearson's r is not
normal, (click
here for illustration) the sample
correlations are transformed to Fisher's
z's.
where is
the first correlation transformed to z', is
the second correlation converted to z', and is the standard error of
the difference between z's and is equal to:
where N_{1} is the sample
size for the first correlation and N_{2} is the sample size
for the second correlation.