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 \(Y\)?"