Compositional Non-parametric Tests


Compositional Non-parametric Tests

van den Boogaart, K. G.; Tolosana-Delgado, R.

Current compositional methods typically rely on some sort of normality hypothesis for testing. Typical well-known non-parametric tests rely on ranks transforms, which are undefined for multivariate problems. The aim of this contribution is thus to investigate the possibilities for truly multivariate non-parametric tests of location and distribution for compositonal data. The challenge is the to ensure subcompositional coherence, which would bring the possibility to attribute deviations to certain subcompositions.

For the case of tests for a known compositional mean, we propose a bootstrap method, measuring how extreme this mean is with respect to a bootstrap sample of the empirical compositional mean. The extremity is checked in each of the pairwise log-ratios. This ensures a subcompositional coherence in the sense that a rejected hypothesis will always be rejected in at least one subcomposition.

For the case of a two sample test comparing two populations, the same principle can be extended. The mean difference is compared with bootstrap samples of mean differences. The same subcompositional coherence applies.

For multiple samples we can extend the idea of ANOVA of measuring the variability of the group means. The variability is measured in terms of the variation matrix. For each entry of the variatin matrix we quantify its quantile in the bootstrap population. We take then the maximum of the quantiles and bootstrap this maximum. In this way we again get a subcompositionally test for equal mean in all samples. Weighted modifications might improve power of the test in case of unequal sample sizes.

  • Lecture (Conference)
    CoDaWork 2017, 06.-9.6.2017, Abbadia San Salvatore, Italia

Permalink: https://www.hzdr.de/publications/Publ-24847
Publ.-Id: 24847