The sampling distribution of the difference between two independent Pearson r's can be approached in terms of the sampling distribution of z'. First both r's are converted to z'. The standard error of the difference between independent z's is:

where N

Assume that in the population of females the correlation between a test of verbal ability and a test of spatial ability is 0.6 whereas in the population of males the correlation is 0.5. If a random sample of 40 females and 35 males is taken, what is the probability that the correlation for the female sample will be lower than the correlation for the male sample.