Confidence Interval, Difference between Independent Correlations (1 of 4)
The procedure for computing a confidence interval on the difference between two independent correlations is similar to the procedure for computing a confidence interval on one correlation. The first step is to convert both values of r to z'. Then a confidence interval is constructed based on the general formula for a confidence interval where the statistic is z'1 - z'2 , and the standard error of the statistic is:
where N1 is the number of pairs of scores in r1 and N2 is the number of pairs of scores in r2. Once the confidence interval is computed, the upper and lower limits are converted back from z' to r. As an example, assume a researcher were interested in whether the correlation between verbal and quantitative SAT scores (VSAT and QSAT) is different for females than it is for males. Samples of 80 females and 75 males are tested and the correlation for females is 0.55 and the correlation for males is 0.42.