# Fisher r-to-z transformation: comparison of non-significant rs

#### jstorc

##### New Member
Dear readers, I would like to ask you whether it makes sense to compare two correlation coefficients, ra and rb, found in two independent samples, using the Fisher r-to-z transformation, whereby ra or rb or both ra and rb are non-significant. In my view, a necessary condition for such a comparison is that *both* rs are significant at a specific significance level - not necessary at the same significance level.

Last edited:

#### katxt

##### Active Member
I think the statistics works. It is certainly possible that a true weak positive correlation and a true weak negative correlation can be shown to be different, while at the same neither correlation can be shown different from 0 from the data. However, the difference may be too small to be of practical significance.
A "significant" correlation means significantly different from 0, What would you say if ra and rb were both not significantly different from 0.5. Would you be happy to test between them?

#### jstorc

##### New Member
I think the statistics works. It is certainly possible that a true weak positive correlation and a true weak negative correlation can be shown to be different, while at the same neither correlation can be shown different from 0 from the data. However, the difference may be too small to be of practical significance.
A "significant" correlation means significantly different from 0, What would you say if ra and rb were both not significantly different from 0.5. Would you be happy to test between them?
I am not a statistician but as I see in my data, in the first group there is a strongly negative partial correlation that is not significant (p>.05) and in the second group a very weak negative partial correlation that is strongly significant (p<.01). The only difference I can discern, is that the sample size of the first group is too low (N<20) and the sample size of the second group is too high (N>2000). I infer from this that the significance level licenses the z difference with reference to sample size. Accordingly, in the first group with N<20 I need more cases to get a significant r and accept the z value as reliable.

Last edited:

#### katxt

##### Active Member
OK. Sample size certainly can reduce the power to distinguish between the two correlations, but I still think that it is valid to test. Are you hoping that they are different, or the same?
In any event, if you're not comfortably with testing, don't. Report "no sig diff" bearing in mind that this is really means "I don't know if they are different or not". kat

#### jstorc

##### New Member
OK. Sample size certainly can reduce the power to distinguish between the two correlations, but I still think that it is valid to test. Are you hoping that they are different, or the same?
In any event, if you're not comfortably with testing, don't. Report "no sig diff" bearing in mind that this is really means "I don't know if they are different or not". kat
Thank you.