# Solved – 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

Contents

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.)

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