Applications of Permutation Methods in the Analysis of Associations

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.