# I have a statistic, how do I calculate its distribution?

I am comparing images for correlation. The images are all correlated, but I would like to determine when one pair is much more highly correlated, relative to another pair. I am using as a statistic the difference in the logs of p-values produced by a Spearman rank correlation test. If this is difference is small, there is a normal degree of correlation. If this difference is big, there is a higher degree of correlation in one pair than the other pair.

Let $A$, $B$, and $C$ be images. I would like to determine a distribution and calculate a p-value for $x = \vert \log(\mbox{SpearmanRankCorr}(A,B)) - \log(\mbox{SpearmanRankCorr}(A,C)) \vert$

• Have you considered bootstraping? Mar 7, 2017 at 14:52

• Is this the only way to go about determining a distribution from a statistic? If I try to perform, $$f_{Y}(y) = f_{X}(g^{-1}(y)) \bigl\vert \dfrac{d}{dy}g^{-1}(y) \bigr\vert,$$ any statistic $Y = g(X)$ of the data, $X$, involving the Spearman rank correlation test will not be one-to-one. Assuming I had a statistic, $g(X)$, that was invertible, the underlying data, $X$, is image data that doesn't follow any simple distributions. (I guess I could model it as a complicated mixture of Gaussians, right?) Is there any other way to describe a distribution of an arbitrary statistic? Apr 25, 2012 at 22:09