# Explaining the difference between Pearson correlation and distance correlation

This question and its answer might highlight my naivete regarding Brownian/distance correlation.

I'm using the difference between a matrix of distance correlations, as calculated by energy::dcor(), and absolute value Pearson correlations, as calculated by cor(), to highlight potential nonlinear dependencies introduced with a certain estimation technique.

In my resulting difference matrix, I have a handful of negative values indicating that the Pearson correlation is larger in magnitude than the distance correlation (range from -.07 to -.01).

First, is my approach adequate? If so, how do I explain why the Pearson correlations might be larger in magnitude than distance correlation?

• For a bit of clarification: My understanding of distance correlation is that dCor = 1 (and r = 1) when two variables are perfectly co-linear. However, as you can see via this demonstration link versus the identical for Pearson [link] (en.wikipedia.org/wiki/Correlation_and_dependence#/media/…), the correlation index for the very strongly dependent linear data is lower for distance correlations. Why? – topherwhatever Mar 11 at 13:22