energy (version 1.6.2)

dcor.ttest: Distance Correlation t-Test


Distance correlation t-test of multivariate independence.


dcor.ttest(x, y, distance=FALSE) dcor.t(x, y, distance=FALSE) bcdcor(x, y, distance=FALSE)


data or distances of first sample
data or distances of second sample
logical: TRUE if x and y are distances


dcor.t returns the t statistic, bcdcor returns the bias corrected dcor statistic, and dcor.ttest returns a list with class htest containing
description of test
observed value of the test statistic
degrees of freedom
(bias corrected) dCor(x,y)
p-value of the t-test
description of data


dcor.ttest performs a nonparametric t-test of multivariate independence in high dimension (dimension is close to or larger than sample size). The distribution of the test statistic is approximately Student t with $n(n-3)/2-1$ degrees of freedom and for $n \geq 10$ the statistic is approximately distributed as standard normal. dcor.t returns the t statistic and bcdcor returns the bias corrected distance correlation statistic. The sample sizes (number of rows) of the two samples must agree, and samples must not contain missing values. Arguments x, y can optionally be dist objects or distance matrices (in this case set distance=TRUE). The t statistic is a transformation of a bias corrected version of distance correlation (see SR 2013 for details). Large values (upper tail) of the t statistic are significant.


Szekely, G.J. and Rizzo, M.L. (2013). The distance correlation t-test of independence in high dimension. Journal of Multivariate Analysis, Volume 117, pp. 193-213.

Szekely, G.J., Rizzo, M.L., and Bakirov, N.K. (2007), Measuring and Testing Dependence by Correlation of Distances, Annals of Statistics, Vol. 35 No. 6, pp. 2769-2794.

Szekely, G.J. and Rizzo, M.L. (2009), Brownian Distance Covariance, Annals of Applied Statistics, Vol. 3, No. 4, 1236-1265.

See Also

dcov.test dcor DCOR


Run this code
 x <- matrix(rnorm(100), 10, 10)
 y <- matrix(runif(100), 10, 10)
 dx <- dist(x)
 dy <- dist(y)
 dcor.t(x, y)
 bcdcor(dx, dy, distance=TRUE)
 dcor.ttest(x, y)

Run the code above in your browser using DataLab