I am comparing Spearman correlation coefficients for two overlapping correlations based on dependent groups. There is quite a bit of literature on comparing correlations for Pearson's coefficients but mixed suggestions when comparing Speaman coefficients. From my understanding one suggested method is to use the Fisher z- transformation to covert the Spearman coefficients and then tested.

I was referred to the web-based GUI cocor R package (http://comparingcorrelations.org/) for comparing the correlation coefficients and see a number of tests that are conducted and reported. Specifically some convert and use the transofrmation. My question is, when multiple results are reported which, if any, is the standard for reporting? The results indicate:

-Pearson and Filon's z test

- Olkin's z test

- Steiger's modification of Dunn and Clark's z test

-Meng, Rosenthal, and Rubin's z test

-Hittner, May, and Silver's modification of Dunn and Clark's z (1969) using a backtransformed average Fisher's Z procedure

-Zou's confidence interval

All the tests are indicating the same result (whether the null hypothesis, hypothesized difference between correlation coeffiecients is 0, are retained or rejected). Which is the standard to report? I am a bit lost and unable to find much consistent literature. Any help would be appreciated!