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Kendall's tau rank correlation

Source: R/rank.R
tau.Rd

Kendall's \(\tau\) measures the rank concordance between two variables — for distribution dynamics, typically a set of units' values at two points in time. It is the (concordant minus discordant) pair count, normalised, and is a natural summary of positional (exchange) mobility: \(\tau = 1\) means ranks are perfectly preserved, \(\tau = -1\) a complete reversal, and \(\tau \approx 0\) extensive rank shuffling. Ties are handled with the tau-b correction.

Usage

tau(x, y)

Arguments

x, y

Numeric vectors of equal length.

Value

An object of class sddr_tau: a list with the statistic tau, the concordant and discordant pair counts, an asymptotic (normal) two-sided p_value, and n.

References

Kendall, M. G. (1938). A new measure of rank correlation. Biometrika, 30(1/2), 81-93. doi:10.2307/2332226

See also

theta()

Examples

set.seed(1)
x <- rnorm(30)
y <- x + rnorm(30)          # correlated ranks
tau(x, y)
#> <sddr> Kendall's tau
#>   tau = 0.5126  (concordant 329, discordant 106, n = 30)
#>   asymptotic two-sided p-value = 6.934e-05