Comparing Correlation Coefficients
When conducting correlation analyses with two independent groups of different sample sizes, researchers typically compare the two correlations. Researchers recommend this comparison when correlations on the same variables are statistically significant in both groups. The way to do this is by transforming the correlation coefficient values, or r values, into z scores. They use Fisher’s r to z transformation to compare z scores. And also, they assess statistical significance by calculating the observed z test statistic.
Using the observed z test statistic (z_observed) at a set alpha level, researchers can assess statistical significance. SPSS does not perform this analysis, so you can conduct it manually or use an online calculator instead. Run the correlation analyses between the two groups and calculate their correlation coefficients (r), ignoring negative signs. The next step is to note, or write down, the sample sizes per each independent group. Use a chart or online calculator to find the z values (z1 and z2) for the correlation coefficients (r). An online calculator typically calculates significance once you enter the two correlation values and sample sizes (N1 and N2). Instead of using an online calculator, you can use a statistical chart with z values and a calculator to implement the following formula:
Zobserved = (z1 – z2) / (square root of [ (1 / N1 – 3) + (1 / N2 – 3) ]
After determining the observed z value, assess statistical significance by checking if it exceeds the critical value. For example, if the observed value was zobserved = -1.97 and your level of significance is set at .05, which indicates that the critical value is ± 1.96, your zobserved falls into the rejection region and is greater than your critical value; thus, statistical significance. You can reject the null hypothesis that the two correlations are not significantly different.
Take the Course: Correlational Research Design