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Intuitively, the Kendall correlation between two variables will be high when observations have a similar (or identical for a correlation of 1) rank (i.e. relative position label of the observations within the variable: 1st, 2nd, 3rd, etc.) between the two variables, and low when observations have a dissimilar (or fully different for a ...
Some of the more popular rank correlation statistics include Spearman's ρ; Kendall's τ; Goodman and Kruskal's γ; Somers' D; An increasing rank correlation coefficient implies increasing agreement between rankings. The coefficient is inside the interval [−1, 1] and assumes the value:
In statistics, Spearman's rank correlation coefficient or Spearman's ρ, named after Charles Spearman [1] and often denoted by the Greek letter (rho) or as , is a nonparametric measure of rank correlation (statistical dependence between the rankings of two variables).
Spearman's rank correlation coefficient is a measure of how well the relationship between two variables can be described by a monotonic function. The Kendall tau rank correlation coefficient is a measure of the portion of ranks that match between two data sets.
Either Pearson's , Kendall's τ, or Spearman's can be used to measure pairwise correlation among raters using a scale that is ordered. Pearson assumes the rating scale is continuous; Kendall and Spearman statistics assume only that it is ordinal.
Kendall's W (also known as Kendall's coefficient of concordance) is a non-parametric statistic for rank correlation. It is a normalization of the statistic of the Friedman test, and can be used for assessing agreement among raters and in particular inter-rater reliability. Kendall's W ranges from 0 (no agreement) to 1 (complete agreement).
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Rank correlation coefficients, such as Spearman's rank correlation coefficient and Kendall's rank correlation coefficient (τ) measure the extent to which, as one variable increases, the other variable tends to increase, without requiring that increase to be represented by a linear relationship.