# Is there an easy way to calculate significant difference between two largely overlapping correlations from same sample?

I am comparing three different measures comprised of 10-20 items each. Each of these measures is actually a short form of a longer 40-item measure and each of the short forms shares some similar items, and thus they are quite similar. I am interested in seeing how each of these short forms are correlated with the same dependent variable.

I come up with r= .54, .56, and .58.

How can I assess whether these correlations are significantly different? It seems doing a simple r-to-z transformation would not be appropriate since the independent variables are quite similar and the dependent variable is in fact the same for all three correlations. As such, all of these *r*s overlap quite a bit.

I found this one paper:

Zou, G. (2007). Toward using confidence intervals to compare correlations. Psychological Methods, 12(4), 399.

But it seems way over my head and I am wondering whether there is an easier way to do it...

Any guidance would be appreciated!

• My thinking is that those correlations are all too close to each other to detect a difference statistically for the given small sample size. – Michael R. Chernick May 29 '12 at 20:18
• Based on the abstract the Zou paper does look dead-on as one that would address your problems. If the fact that the 3 scores share some components makes you leery of using Fisher's Z transformation, the same problem would seem to apply to a regression approach. – rolando2 Jan 26 '13 at 1:10

A bit more meaningful may be to fit 3 regression model, each using one of the measures and your dependent variable, then plot the 3 pairwise scatterplots of the fitted(predicted) values. This is best done with an aspect ratio of 1 in a square plot and with an $y=x$ reference line. This can show that the 3 measures give essentially the same predictions, or if not can show where they differ.