Sampling Distribution of the Difference Between Independent Pearson r's (2 of 2)
Next section: Median
Start by computing the mean and standard deviation
of the sampling distribution of the difference between z's. As can be calculated
with the help of the r to z' procedure, r's of .6 and .5 correspond to
Z's of .69 and .55 respectively. Therefore the mean of the sampling distribution
is:
0.69-0.55 = 0.14.
The standard deviation is:
The
portion of the distribution for which the difference is negative (the
correlation in the female sample is lower) is shaded. What proportion
of the area is this?
A difference of 0 is: 
standard
deviations above (0.58 sd's below) the mean. A z
table can
be used to calculate that the probability of a z less than or equal to
-0.58 is 0.28. Therefore the probability the the correlation will be lower
in the female sample is 0.28.
Next section: Median