# What is a measure of association that conveys actual similarity of values between two variables and not just correlation?

Background: I would like to offer readers a statistic that conveys the similarity of two sets of numbers. I thought that I had what I needed with correlation coefficient (indeed, I have a coefficient of determination/r2 of 98.7). But I've just realized that r and r2 conveys only that the two sets of numbers are correlated in their upward and downward movement; and what I want (also) to convey is that they are also very nearly identical. But yet I feel like regression analysis is more than I need (or, more precisely, more than I can do with Excel). To be a little more concrete, imagine a data set with monthly earnings for two stores in a strip mall. Correlation coefficients would capture whether the stores' earnings were covariate. But I want to demonstrate also that the monthly earnings also happen to be very nearly the same actual number. On a graph, they are visually one is on top of the other. But is there a statistical metric that captures that?

Question: What is a measure of association that conveys actual similarity of values between two variables and not just correlation?

• You probably want to take the average of the absolute value of the differences - otherwise $(0, 10)$ and $(10, 0)$ are considered identical. This is known as the $\ell_1$ distance; you could also try the $\ell_2$, the square root of the mean of the squared distances. – Dougal Aug 7 '14 at 4:04