Taujärjestyskorrelaatiokerroin

Taujärjestyskorrelaatiokerroin, often referred to as Kendall's tau, is a non-parametric measure of the ordinal association between two measured quantities. It is a statistical measure used to assess the similarity of the orderings produced by two different ranking methods. Essentially, it calculates how concordant or discordant pairs of observations are when ranked according to two different variables.

The coefficient ranges from -1 to +1. A tau of +1 indicates perfect agreement between the two rankings, meaning that for every pair of items, the order is the same for both rankings. Conversely, a tau of -1 indicates perfect disagreement, where the order is exactly reversed for every pair. A tau of 0 suggests no association between the rankings.

Kendall's tau is calculated by comparing all possible pairs of observations. For each pair, it's determined if they are concordant (both rankings agree on the order) or discordant (the rankings disagree on the order). The formula involves the number of concordant pairs (C), the number of discordant pairs (D), and the total number of pairs (n(n-1)/2). The most common version, Kendall's tau-b, corrects for ties in the rankings. Tau is less sensitive to outliers than Pearson's correlation coefficient and is suitable for smaller sample sizes or when the data does not meet the assumptions of parametric tests.