Applications of Permutation Methods in the Analysis of Associations

Grzegorz Kończak


Objective: The permutation model in hypothesis testing was introduced by R. A. Fisher in 1925. These methods permit us to test hypotheses with as minimal assumptions as possible. The tests require high computing power and therefore have found greater application in recent years. However, the concept of permutation methods is much wider than the issue of permutation testing. In 1923 J. Spława-Neyman introduced a permutation model for the analysis of field experiments. The purpose of the article is to present the possibilities of applying permutation methods in the analysis of dependencies. The article presents selected possibilities of data rearranging in dependency analysis.

Research Design & Methods: The study considered the analysis of multivariate data. The paper presents theoretical considerations and refers to the Monte Carlo simulation.

Findings: A proposed method to allow investigation of the significance of the relationship between two data sets is presented. The considerations are supplemented by comparing the size and power of the proposed test with tests known from canonical correlation analysis.

Implications/Recommendations: The proposal is most powerful for non-normally distributed variables and small samples.

Contribution: The proposed test can be used in the analysis of multidimensional economic and social phenomena.


permutation methods, data labels permutation, association analysis, canonical correlations

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Berry, K. J., Johnston, J. E. and Mielke Jr., P. W. (2014) A Chronicle of Permutation Statistical Methods. New York: Springer International Publishing.

Berry, K. J., Johnston, J. E. and Mielke Jr., P. W. (2018) The Measurement of Association. A Permutation Statistical Approach. Cham: Springer Nature Switzerland.

Berry, K. J., Mielke Jr., P. W. and Johnston, J. E. (2016) Permutation Statistical Methods. An Integrated Approach. Cham: Springer Nature Switzerland.

Corain, L., Arboretti, R. and Bonnini, S. (2016) Ranking of Multivariate Populations. A Paermutation Approach with Applications. Boca Raton: CRC Press.

Good, P. (2005) Permutation, Parametric and Bootstrap Tests of Hypotheses. New York: Springer Science Business Media.

Ledwina, T. (2012) “Neyman Jerzy (1894–1981)” in: Statystycy polscy. Warszawa: Główny Urząd Statystyczny, Polskie Towarzystwo Statystyczne.

Lehmann, E. L. and Romano, J. P. (2005) Testing Statistical Hypotheses. New York: Springer-Verlag.

Mielke, P. W. and Berry K. J. Jr. (2007) Permutation Methods. A Distance Function Approach. New York: Springer Science+Business Media.

O’Gorman, T. W. (2012), Adaptive Tests of Significance Using Permutations of Residuals with R and SAS. John Wiley and Sons.

Rencher, A. C. and Christensen, W. F. (2012) Methods of Multivariate Analysis. Hoboken: Wiley.

Spława-Neyman, J. (1923) “Próba uzasadnienia zastosowań rachunku prawdopodobieństwa do doświadczeń polowych”. Rocznik Nauk Rolniczych 10: 1–51.

Thompson, B. (1984) Canonical Correlation Analysis: Uses and Interpretation. London: Sage Publications.