Definition

  • two series of data: $X$ and $Y$
  • cooccurance of them: $(x_i, x_j)$, and we assume that $i<j$
  • concordant: $x_i < x_j$ and $y_i < y_j$; $x_i > x_j$ and $y_i > y_j$; denoted as $C$
  • discordant: $x_i < x_j$ and $y_i > y_j$; $x_i > x_j$ and $y_i < y_j$; denoted as $D$
  • neither concordant nor discordant: whenever equal sign happens

Kendall’s tau is defined as