｛n（n-1）｝/2

问题如下：

Find Kendall’s Tau for the following data:

解释：

The first step is to rank the data:

The next step is to see which pairs are concordant, which are discordant, and which are neither.

Which leads to the pair-by-pair comparison:

For the first observation, because both the rank of X & Y are the maximum, every other observation will automatically be concordant with respect to this one. By contrast, looking at the second and third observations, the X rank increases while the Y rank decreases. Therefore, this pair is discordant.

$\widehat\tau=\frac{n_c-n_d}{n(n-1)/2}=(5-5)/10=0$