I have a set of scores on a specific dataset given by human evaluators, let's call it HJ
. I also have the scores of two computer models on the same dataset, let's call these sets M1
and M2
. I have calculated Spearman's coefficients for (HJ,M1)
and (HJ,M2)
, which show that M2
is closer to human judgements than M1
. Now I've been asked to find out if the difference between these two rho coefficients is statistically significant. My statistical knowledge is limited, so any help on how I could do that would be highly appreciated.
EDIT:
In the book "Applied Multiple Regression/Correlation Analysis for the Behavioural Sciences" (Cohen and Cohen, 1975), I found the following $t$-statistic formula for cases identical to the one I describe above, but for Pearson coefficients:
$$ t=\frac{(r_{XY}-r_{VY})\sqrt{(n-3)(1+r_{XV})}}{\sqrt{2(1-r^2_{XY}-r^2_{VY}-r^2_{XV}+2r_{XY} r_{XV} r_{VY})}} $$
where $r_{XY}$ is the correlation between $X$ and $Y$ and $n$ is the sample size. Is this also applicable to rank correlations? For a 2-tailed $t$-test it gives different results than the permutation test suggested by Greg below (in case I ask something trivial please excuse my ignorance).