Performs Energy statistics distance components (DISCO) multi-sample tests (Rizzo and Székely, 2010). The implementation here uses the disco implementation from the energy package.
DISCOF(X1, X2, ..., n.perm = 0, alpha = 1, seed = 42)An object of class disco with the following components:
The function call
Description of the test
Vector of observed values of the test statistic
Vector of Bootstrap p values
Number of samples
Number of observations
Between-sample distance components
One-way within-sample distance components
Within-sample distance component
Total dispersion
Degrees of freedom for treatments
Degrees of freedom for error
Alpha (exponent on distance)
Factor names
Factor levels
Sample sizes
Matrix containing decomposition
First dataset as matrix or data.frame
Second dataset as matrix or data.frame
Further datasets as matrices or data.frames
Number of permutations for Bootstrap test (default: 0, no Bootstrap test performed)
Power of the distance used for generalized Energy statistic (default: 1). Has to lie in \((0,2]\). For values in \((0, 2)\), consistency of the resulting test has been shown.
Random seed (default: 42)
| Target variable? | Numeric? | Categorical? | K-sample? |
| No | Yes | No | Yes |
DISCO is a method for multi-sample testing based on all pairwise between-sample distances. It is analogous to the classical ANOVA. Instead of decomposing squared differences from the sample mean, the total dispersion (generalized Energy statistic) is composed into distance components (DISCO) consisting of the within-sample and between-sample measures of dispersion.
DISCOF is based on the DISCO F ratio of the between-sample and within-sample dispersion. Note that the F ration does not follow an F distribution, but is just called F ratio analogous to the ANOVA.
In both cases, small values of the statistic indicate similarity of the datasets and therefore, the null hypothesis of equal distributions is rejected for large values of the statistic.
This implementation is a wrapper function around the function disco that modifies the in- and output of that function to match the other functions provided in this package. For more details see the disco.
Szekely, G. J. and Rizzo, M. L. (2004) Testing for Equal Distributions in High Dimension, InterStat, November (5).
Rizzo, M. L. and Szekely, G. J. (2010). DISCO Analysis: A Nonparametric Extension of Analysis of Variance, Annals of Applied Statistics, 4(2), 1034-1055. doi:10.1214/09-AOAS245
Szekely, G. J. (2000) Technical Report 03-05: E-statistics: Energy of Statistical Samples, Department of Mathematics and Statistics, Bowling Green State University.
Rizzo, M., Szekely, G. (2022). energy: E-Statistics: Multivariate Inference via the Energy of Data. R package version 1.7-11, https://CRAN.R-project.org/package=energy.
Stolte, M., Kappenberg, F., Rahnenführer, J., Bommert, A. (2024). Methods for quantifying dataset similarity: a review, taxonomy and comparison. Statist. Surv. 18, 163 - 298. tools:::Rd_expr_doi("10.1214/24-SS149")
DISCOB, Energy
# Draw some data
X1 <- matrix(rnorm(1000), ncol = 10)
X2 <- matrix(rnorm(1000, mean = 0.5), ncol = 10)
# Perform DISCO tests
if(requireNamespace("energy", quietly = TRUE)) {
DISCOF(X1, X2, n.perm = 100)
}
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