Significance test on the difference of Spearman's correlation coefficient

Question

I have got a human-rated set of ranking (HUMAN-RANKING), a set of ranking generated by the presently used, popular method (PRESENT-RANKING), and finally a set of ranking generated by my purposed method (MY-RANKING).

I calculated the Spearman's correlation between HUMAN-RANKING and PRESENT-RANKING. Let me call this: HUMAN-PRESENT-SPEARMAN.

I then found out the Spearman's correlation between HUMAN-RANKING and MY-RANKING. Let me call this: HUMAN-MY-SPEARMAN.

How can I find out if the difference between HUMAN-MY-SPEARMAN and HUMAN-PRESENT-SPEARMAN is statistically significant?

Thanks in advance.

Answer 1

You can do what is called Fisher transformation. A link can be found here.

One issue is that the Fisher transformation assumes statistical independence but since you are using HUMAN-RANKING in both correlations, that assumption is violated. I'm not sure what the consequences are from violating that assumption.

Just realized this was from October so it probably isn't helpful to you, but I had already written the post. Cheers.