Tests for Categorical Data Beyond Pearson: A Distance Covariance and Energy Distance Approach
- 1Biostatistics Department German Cancer Research Center (DKFZ) Heidelberg Baden‐Württemberg Germany
- 2Department of Statistics, Faculty of Mathematics University of Santiago de Compostela Santiago de Compostela Galicia Spain
- 3Psychiatric Genetics Laboratory, Santiago Health Research Institute (IDIS) University Hospital Santiago de Compostela Galicia Spain
Abstract
Categorical variables are of uttermost importance in biomedical research. When two of them are considered, it is often the case that one wants to test whether or not they are statistically dependent. We show weaknesses of classical methods—such as Pearson's and the ‐test—and we propose testing strategies based on distances that lack those drawbacks. We first develop this theory for classical two‐dimensional contingency tables, within the context of distance covariance, an association measure that characterizes general statistical independence of two variables. We then apply the same fundamental ideas to one‐dimensional tables, namely, to the testing for goodness of fit to a discrete distribution, for which we resort to an analogous statistic called energy distance. We prove that our methodology has desirable theoretical properties, and we show that we can calibrate the null distribution of our test statistics without resampling. We illustrate all this in simulations, as well as with some real data examples, demonstrating the adequate performance of our approach for biostatistical practice.
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BibTeX
@article{castroprado2026tests,
title = {{Tests for Categorical Data Beyond Pearson: A Distance Covariance and Energy Distance Approach}},
author = {Fernando Castro-Prado and Wenceslao González–Manteiga and Javier Costas and Fernando Facal and Dominic Edelmann},
journal = {Biometrical Journal},
year = {2026},
month = jun,
doi = {10.1002/bimj.70129},
url = {https://doi.org/10.1002/bimj.70129},
note = {CC BY},
}
RIS
TY - JOUR
TI - Tests for Categorical Data Beyond Pearson: A Distance Covariance and Energy Distance Approach
AU - Fernando Castro-Prado
AU - Wenceslao González–Manteiga
AU - Javier Costas
AU - Fernando Facal
AU - Dominic Edelmann
PY - 2026
DA - 2026/06/01
JO - Biometrical Journal
DO - 10.1002/bimj.70129
UR - https://doi.org/10.1002/bimj.70129
AB - Categorical variables are of uttermost importance in biomedical research. When two of them are considered, it is often the case that one wants to test whether or not they are statistically dependent. We show weaknesses of classical methods—such as Pearson's and the ‐test—and we propose testing strategies based on distances that lack those drawbacks. We first develop this theory for classical two‐dimensional contingency tables, within the context of distance covariance, an association measure that characterizes general statistical independence of two variables. We then apply the same fundamental ideas to one‐dimensional tables, namely, to the testing for goodness of fit to a discrete distribution, for which we resort to an analogous statistic called energy distance. We prove that our methodology has desirable theoretical properties, and we show that we can calibrate the null distribution of our test statistics without resampling. We illustrate all this in simulations, as well as with some real data examples, demonstrating the adequate performance of our approach for biostatistical practice.
SN - 0323-3847
SN - 1521-4036
ER -