# spearman's rank correlation coefficient

- Measures how much the
*rankings*between \(X\) and \(Y\) match. Here,*rank*refers to the ordering of the values: first, second, third, etc. - So, if the point with the smallest \(X\) is also the point with the smallest \(Y\), and the point with the second-smallest \(X\) is also the point with the second-smallest \(Y\), and so on,… then the spearman coefficient is 1
- Alternatively, say that the spearman coefficient is the pearson correlation coefficient of the rank-values
- Alternatively, see that the spearman coefficient measures to what degree the relationship between \(X\) and \(Y\) can be expressed by a monotonic function

## 1. relationship between correlation coefficient

- correlation coefficient asks: "Is there a linear relationship between \(X\) and \(Y\)?"
- spearman's asks: "Is there a monotonic relationship between \(X\) and \(Y\)?"