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