# Statistical test for comparing means of correlation coefficients

#### killver

##### New Member
Suppose that I have two lists of correlation coefficients such as A = [0.5,0.3,0.25,0.3,-0.1] and B = [0.8,0.7,0.75,0.8,0.8]. The correlation coefficients in A are independent to B.

Now, I want to test the null hypothesis, that the means of both lists are equal.

I am familiar with how to test this hypothesis for single correlation coefficients by doing a Fisher z transformation and a subsequent z-test. However, I am unsure how to do that for the mean of coefficients.

My approach would be to again do Fisher transformation. Then determine the mean of the transformed correlations and perform a z-test for the means.

Any ideas?

#### PeterFlom

##### New Member
You can treat the two sets of numbers as just sets of numbers. Thus, you can do a t-test (but check the assumptions) or any non-parametric test of difference (e.g. Mann Whitney U) or a permutation test would work too.

#### Karabiner

##### TS Contributor
Suppose that I have two lists of correlation coefficients such as A = [0.5,0.3,0.25,0.3,-0.1] and B = [0.8,0.7,0.75,0.8,0.8]. The correlation coefficients in A are independent to B.
And all correlation coefficients with group B are completely independent from each other?

Where do all those coefficients come from, what is it all about?

With kind regards

K.

#### killver

##### New Member
You can treat the two sets of numbers as just sets of numbers. Thus, you can do a t-test (but check the assumptions) or any non-parametric test of difference (e.g. Mann Whitney U) or a permutation test would work too.
Correlation coefficients are not distributed normally as far as I know. So a t-test would not work. A fisher transformation could help though but then you can do a z test in my opinion.

And all correlation coefficients with group B are completely independent from each other?

Where do all those coefficients come from, what is it all about?

With kind regards

K.

Okay, let me go through a quick concrete example.

Suppose I have five different subjects (or datasets or whatever). For each subject I measure four vectors A, B, C and D. For each subject I calculate the correlation coefficient between A and B (I call this AB) and C and D (I call this CD). Both correlation coefficients are independent.

Now, I can calculate these two correlation coefficients for each single subject leading to my two vectors of correlation coefficients where each element of the vectors correspond to the coefficient between AB or CD for a single subject i.

Now I want to know whether the two vectors (means of vectors) are similar.

It is basically just an extension of the regular significance test of similarity for single correlation coefficients. But now, I want to know whether this holds across subjects.

I hope this makes it clearer.

#### killver

##### New Member
I hope pushing is allowed here!

PUSH #### Karabiner

##### TS Contributor
So you have n subjects, each with 2 measurements
(correlation AB and correlation CD). As Peter Flom
said, you can treat those measurements just like
any numbers. If n is small, you could use the Wilcoxon
signed rank test, otherwise dependent samples t-test.

With kind regards

K.

#### killver

##### New Member
So you have n subjects, each with 2 measurements
(correlation AB and correlation CD). As Peter Flom
said, you can treat those measurements just like
any numbers. If n is small, you could use the Wilcoxon
signed rank test, otherwise dependent samples t-test.

With kind regards

K.
Without Fisher z transformation?