Spearman’s correlation coefficient is a statistical measure of the strength of a ** monotonic relationship between paired data**.

As to two paired data \(R\) and \(S\). The count in them is \(n\). Spearman’s correlation coefficient is defined as:

Here

\[D^2 = (R_i-S_i)^2\]

You should notice: \(R\) and \(S\) are rank.

* r_{s}* is in:

-1 ≤ * r_{s}* ≤ 1

where** | r_{s}|** is

**0 -0.19 ** “very weak”

**0.20 -0.39** “weak”

**0.40 – 0.59** “moderate”

**0.60 – 0.79** “strong”

**0.80 – 1.0** “very strong”

So the ** | r_{s}|** value of pair (

**) is closed to 1, whic means they are strong monotonicity.**

*x, y*The bigger of ** | r_{s}|** the better.