  We present a novel method for testing the hypothesis of equality of two
correlation matrices using paired high-dimensional datasets. We consider test
statistics based on the average of squares, maximum and sum of exceedances of
Fisher transform sample correlations and we derive approximate null
distributions using asymptotic and non-parametric distributions. Theoretical
results on the power of the tests are presented and backed up by a range of
simulation experiments. We apply the methodology to a case study of colorectal
tumour gene expression data with the aim of discovering biological pathway
lists of genes that present significantly different correlation matrices on
healthy and tumour samples. We find strong evidence for a large part of the
pathway lists correlation matrices to change among the two medical conditions.
