# Relationships between variables (correlation)

## Overview

This tutorial takes a look at how to describe relationships between variables using the correlation coefficient. Essentially there are three well-known correlation coefficients. *Pearson’s correlation coefficient, r* (or Pearson’s product-moment correlation coefficient to give it its full name), is a standardized measure of the strength of relationship between two variables. It can take any value from −1 (as one variable changes, the other changes in the opposite direction by the same amount), through 0 (as one variable changes the other doesn’t change at all), to +1 (as one variable changes, the other changes in the same direction by the same amount). *Spearman’s correlation coefficient* is Pearson’s correlation coefficient performed on data that have been converted into ranked scores. By analyzing ranks it has less-restrictive assumptions than Pearson’s *r*. Finally, *Kendall’s tau* is a non-parametric correlation coefficient similar to Spearman’s correlation coefficient, but is preferred for small data sets with a large number of tied ranks.