I've got four dependent correlations (i.e., from the same sample) that involve predictor variables $(A,B,C,D)$ and an outcome variable $(E)$. $N=172$.
$$\begin{array}{c|cccc}{\rm Statistic}&AE&BE&CE&DE\\\hline r&-.480&.276&.395&.327\\p&< .01&< .01&< .05&< .01\end{array}$$
I am trying to run three chi-square tests on this set of four dependent correlations, where $H_0: r_{AE} = r_{BE} = r_{CE} = r_{DE} = 0$; and $H_1$ is simply "NOT $H_0$". Assuming $H_0$ is rejected, I will then be testing: $H_0: r_{AE} = r_{BE} = r_{CE} = r_{DE}$; with $H_1$ being "NOT $H_0$" again. Assuming that $H_0$ is rejected again, I will then be testing $H_0: r_{BE} = r_{CE} = r_{DE}$.
SPSS cannot help with me comparing dependent correlations and Field's "Discovering Statistics..." (2013) only discusses comparing two dependent correlations, not an entire set. So, I have been directed to several places so far, with no luck:
- "Multicorr" by Steiger (http://www.statpower.net/Software.html). I simply cannot figure out how to use it.
- A paper by Steiger ("Tests for Comparing Elements of a Correlation Matrix", Psychological Bulletin, 1980, 87(2)). But I cannot figure out how/where my numbers fit with the formulas he has provided there.
Ideally, I'd just like the mathematical formula(s) I can use to get my chi-square observed value (I have the critical value tables already). Any guidance that could be offered would be most appreciated.