I am using the mantel.test() function in the "ape" package in R to compare the similarity of two matrices. The function returns a p-value and Z-statistics. While the p-value is understandable, but I am not sure what the significance of the Z-statistics is. i.e Does positive high Z-statistic value means that both matrices are similar, or the similarity can only be described if the p-value is <0.001 and is independent of Z-statistic?
For the Mantel test, the z score is the sum of the products of the corresponding elements of the matrices...so don't confuse it with the standard z-score based on the normal distribution.
The problem with the z-score (sensu Mantel) is that the value depends on the magnitude of your measured variables (kind of like covariance) and is, thus, hard to interpret. So one usually uses a normalized Mantel cofficient, rM, [calculated in the same way as Pearson's product moment correlation coefficient, r,...and interpreted in the same way (on a scale from -1 to 1...albeit the magnitude tends to be downward biased relative to a standard correlation coefficient)]. A positive rM would indicated positive correspondence and a negative rM would indicate a negative correspondence, but be sure to look at the P-value to determine if the value is greater (or less) than would be expected based on the randomized matrices.