Sampling Distribution of the Difference Between Independent Pearson r's (1 of 2)
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 N1 is the number of pairs of scores the first correlation is based on and N2 is the number of pairs of scores the second correlation is based upon. It is important to keep in mind that this formula only holds when the two correlations are independent. This means that different subjects must be used for each correlation. If three tests are given to the same subjects then the correlation between tests one and two is not independent of the correlation between tests one and three.
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.