Τ 等級相關係數

Τ 等級相關係數（τ rank correlation coefficient，${\displaystyle \tau }$）喺統計學上係等級相關嘅一種計法：設 ${\displaystyle (x_{1},y_{1}),...,(x_{n},y_{n})}$ 做一柞個案，每個個案都喺 ${\displaystyle X_{i},Y_{i}}$ 呢兩個變數上有個數值，是但搵兩個個案 ${\displaystyle (x_{i},y_{i})}$ 同 ${\displaystyle (x_{j},y_{j})}$ 嚟睇，佢哋可以係一致（concordant），即係 ${\displaystyle (x_{i}>x_{j})\land (y_{i}>y_{j})}$ 或者 ${\displaystyle (x_{i}<x_{j})\land (y_{i}<y_{j})}$，否則佢哋就算係唔一致（discordant），而 ${\displaystyle \tau }$ 嘅計法如下^[1]：

${\displaystyle \tau ={\frac {({\text{number of concordant pairs}})-({\text{number of discordant pairs}})}{n \choose 2}}}$