# Difference between “common index” and “no common index”

I have been looking at the G*Power tool for Statistical Power Analysis but I am confused by the difference between two of the z-test options.

"Correlations: Two dependent Pearson r's (common index)"


and

"Correlations: Two dependent Pearson r's (no common index)"


Is this in relation to the test data? e.g.

A group of 10 men and a group of 10 women were asked to rate a single index of 10 images (common index)

A group of 10 men and a group of 10 women were asked to rate two separate indexes of images (no common index)

Any help is much appreciated

• Section 26 of the user's manual appears to address this question directly. – whuber Apr 18 '14 at 15:47

From the documentation provided by whuber, it seems that 'index' refers to the indices of $\rho$. In the no-common case:

### 26.3.1 General case: No common index

We want to perform an a priori analysis for a one-sided test whether $\rho_{1,4} = \rho_{2,3}$ or $\rho_{1,4} < \rho_{2,3}$ holds.

And in the common case:

### 26.3.2 Special case: Common index

Assuming again the population correlation matrix $C_p$ shown above, we want to do an a priori analysis for the test whether $\rho_{1,3} = \rho_{2,3}$ or $\rho_{1,} < \rho_{2,3}$ holds. ... we have the following identities: $a = 3$ (the common index) ...

Index in this context refers to the indices of the correlation matrix. The item indexed at $i,j$ gives the correlation between variables $i$ and $j$.

To give a simple example, if you were testing the correlation between height and weight and the correlation between height and arm circumference, they share a common index. If you were comparing the correlations between height, weight and between arm circumference, leg circumference, they do not share a common index.

(Apologies for not using your example; the variables to correlate were unclear to me.)

• @Deepend No problem, glad to help! – Sean Easter Apr 21 '14 at 14:46