Tests of Differences between Independent Pearson Correlations (2 of 5)
-
The third step is to compute the
sample correlations. In this experiment, rengineers = 0.61
and rhumanities = 0.35.
- The fourth step is to compute p, the
probability (or probability value). It is
the probability of obtaining a difference
between the statistic
r1- r2 ( rengineers - rhumanities 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.
The general formula applied to this problem is:
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 N1 is the sample size for the first correlation and N2 is the sample size for the second correlation.