# Comparing correlation coefficients

#### MarieK

##### New Member
Hello,

I have a large sample of patients who have had a TIA, minor stroke or major stroke. I have been looking at correlations in each of these three groups. Is there a statistical test in SPSS (or elsewhere) that would allow me to compare the correlation coefficients between each of three groups in this sample?

Marie

#### spunky

##### Doesn't actually exist
You can do this through Structural Equation Modelling (SEM) by setting up the proper constraints and fitting a multiple-groups model.

But this assumes you know SEM and a software package like R's lavaan or Mplus to fit your SEM-model.

#### Karabiner

##### TS Contributor
Could yo tell something moreabout the study? What are the research questions,
how was the study designed, how were the data collected, how large are the
sample sizes, which variables were correlated and how were they measured?

With kind regards

Karabiner

#### MarieK

##### New Member
I have a group of about 1300 patients who had had disease 1 (subgroup 1), disease 2 (subgroup 2), or disease 3 (subgroup 3).

I have correlated certain biomarkers with their kidney function in the whole group (N=1300), and then in each of these subgroups (N = circa 400 in each subgroup)

e.g. Fibrinogen & GFR

I would like to work out if there is a statistical difference for these correlations across the 3 subgroups (R1 vs R2 vs R3).

The only online calculators that I've found for fisher's z transformation only seem to allow comparison between two correlation coefficients (as opposed to 3 which is what I need).

Is there another link where I could do this or is there any spss syntax that would allow me to do this?

#### MarieK

##### New Member
I have a group of about 1300 patients who had had disease 1 (subgroup 1), disease 2 (subgroup 2), or disease 3 (subgroup 3).

I have correlated certain biomarkers with their kidney function in the whole group (N=1300), and then in each of these subgroups (N = circa 400 in each subgroup)

e.g. Fibrinogen & GFR

I would like to work out if there is a statistical difference for these correlations across the 3 subgroups (R1 vs R2 vs R3).

The only online calculators that I've found for fisher's z transformation only seem to allow comparison between two correlation coefficients (as opposed to 3 which is what I need).

Is there another link where I could do this or is there any spss syntax that would allow me to do this?

#### MarieK

##### New Member
Could yo tell something moreabout the study? What are the research questions,
how was the study designed, how were the data collected, how large are the
sample sizes, which variables were correlated and how were they measured?

With kind regards

Karabiner
I have a group of about 1300 patients who had had disease 1 (subgroup 1), disease 2 (subgroup 2), or disease 3 (subgroup 3).

I have correlated certain biomarkers with their kidney function in the whole group (N=1300), and then in each of these subgroups (N = circa 400 in each subgroup)

e.g. Fibrinogen & GFR

I would like to work out if there is a statistical difference for these correlations across the 3 subgroups (R1 vs R2 vs R3).

The only online calculators that I've found for fisher's z transformation only seem to allow comparison between two correlation coefficients (as opposed to 3 which is what I need).

Is there another link where I could do this or is there any spss syntax that would allow me to do this?

#### katxt

##### Member
You could compare the correlations in pairs using a more stringent significance level (say Bonferroni p<0.05/3 = 0.017).
Or, you could use a permutation test. Use the variance of the three correlations as a measure of how close the three correlations are, and permute the Fibrinogen & GFR pairs across the entire group. See where your correlation variance fits in the generated list. The p value will be the upper tail proportion.
Either way, if you are planning to test other pairs of markers, you will need to make the significance level even lower to avoid false positives.

#### Karabiner

##### TS Contributor
You can compare stabilty of relationship across three groups using linear regression,
but you would have to define a "dependent" and an "independent" variable for each of
these analyses.

The model would look like:
biomarker2 = constant + b1* biomarker1 + b2 * group + b3*(biomarker1*group) + e

The interaction between group and "independent" biomarker tells you whether
the relationship between biomarkers differs between groups.

With kind regards

Karabiner

#### MarieK

##### New Member
Could yo tell something moreabout the study? What are the research questions,
how was the study designed, how were the data collected, how large are the
sample sizes, which variables were correlated and how were they measured?

With kind regards

Karabiner
I have a group of about 1300 patients who had had disease 1 (subgroup 1), disease 2 (subgroup 2), or disease 3 (subgroup 3).

I have correlated certain biomarkers with their kidney function in the whole group (N=1300), and then in each of these subgroups (N = circa 400 in each subgroup)

e.g. Fibrinogen & GFR

I would like to work out if there is a statistical difference for these correlations across the 3 subgroups (R1 vs R2 vs R3).

The only online calculators that I've found for fisher's z transformation only seem to allow comparison between two correlation coefficients (as opposed to 3 which is what I need).

Is there another link where I could do this or is there any spss syntax that would allow me to do this?

You can compare stabilty of relationship across three groups using linear regression,
but you would have to define a "dependent" and an "independent" variable for each of
these analyses.

The model would look like:
biomarker2 = constant + b1* biomarker1 + b2 * group + b3*(biomarker1*group) + e

The interaction between group and "independent" biomarker tells you whether
the relationship between biomarkers differs between groups.

With kind regards

Karabiner
Could I do just do R to Z fisher transformation and then do anova of the Z values? If I do this, should I use bonferroni correction?

Thanks!

#### GretaGarbo

##### Human
Could I do just do R to Z fisher transformation and then do anova of the Z values? If I do this, should I use bonferroni correction?
You can just do the calculation for one correlation at a time and use the Fisher transformation to find out the standard error for that correlation. Then you take the next correlation. You can do that with a pocket calculator.

If you want to compare two korrelations, say corr1 and corr2, or take the difference between them, like

corr1 - corr2

The "uncertainty" in that difference can be:

(corr1 - corr2) +/- 1.96*Sqrt( std(corr1)^2 + std(corr2)^2)

(That would make the strong assumption that the two are not dependent, but maybe this is good enough.)

A possibility is to do bootstrap simulations, but maybe that is too difficult.

Or maybe you can formulate the problem as an anova problem (like the other ones suggested), not dealing with the correlation coefficient at all.