Kendall s tau | Vose Software

Kendall s tau

See also: Modeling correlation introduction, Rank order correlation




Example model

Returns the Kendall tau rank correlation coefficient (a.k.a. Kendall's tau) for a two observed sets of variables.

  • {Var1} - array with observations of one variable.

  • {Var2} - array with observations of another variable.

This is used to measure the degree of correspondence between two variables, for example paired observations. If the correspondence between the two variables is perfect, the coefficient has value 1 and if the disagreement between the two rankings is perfect the coefficient has value -1. For all other arrangements, the value lies between -1 and 1, 0 meaning the variables are completely independent.

Kendall's tau, like Spearman's rho, is carried out on the ranks of the data. That is, for each variable separately the values are put in order and numbered.

An estimate of Kendall's tau for a sample of n observations is given by:

where C is the number of concordant pairs and D the number of discordant pairs. This can also be written as: