ABSTRACT
It is common for a researcher to obtain measurements, in the same sample, on three variables X, Y, and Z (where X and Y may be conceptualised as the independent variables and Z as the dependent variable), in order to study the correlation between X and Z and between Y and Z. In cases like this it is possible to test if the correlation between X and Z is significantly different from the correlation between Y and Z. Here the two correlations are not independent since they have been obtained from the same sample, so we need to use a different approach to the one described in the previous section. Consider an extension of the study on the relationship between degree mark and salary, where the researcher also collects the IQ scores for each subject (see Table 11.5). Let us now consider, for example, that “monthly salary” is the dependent variable Z, and that “degree mark” and “IQ” are the independent variables X and Y, respectively. We already know that the correlation between “degree mark” and “monthly salary” is rxz = 0.778 in this sample, while the correlation between “IQ” and “monthly salary” turns out to be ryz = 0.480. We want to know if the difference between these nonindependent correlation coefficients r is significant.
