A generalised analysis of similarities (ANOSIM) statistic for designs with ordered factors

Somerfield, PJ; Clarke, KR; Gorley, RN. 2021 A generalised analysis of similarities (ANOSIM) statistic for designs with ordered factors. Austral Ecology, 46. 901-910. https://doi.org/10.1111/aec.13043

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Official URL: http://dx.doi.org/10.1111/aec.13043

Abstract/Summary

In the study of multivariate data, for example of change in ecological communities, ANOSIM is a robust non-parametric hypothesis-testing framework for differences in resemblances among groups of samples. RELATE is a non-parametric Mantel test of the hypothesis of no relationship between two resemblance matrices. Details are given of the explicit link between the RELATE statistic, a Spearman rank correlation (ρ) between corresponding elements in the two resemblance matrices, and the ANOSIM statistic R, a scaled contrast between the among- and within-group ranks. It is seen that R can equivalently be defined as the slope of the linear regression of ranked resem�blances from observations against ranked distances among samples, the latter from a simple model matrix assigning the values 1 and 0 to between- and within-group distances, respectively. Re-defining this model matrix to represent ordered distances among groups leads naturally to a generalised ANOSIM statistic, RO, suitable for testing, for example, ordered factor levels in space or time, or an environmental or pollution gradient. Two variants of the generalised ANOSIM statistic are described, namely ROc where there are replicates within groups, and ROs where there are only single samples (no replicates) within groups, for which an ANOSIM test was not previously available. Three marine ecological examples using ANOSIM to analyse an ordered factor in one-way designs are provided. These are: (1) changes in macrofaunal composition with increasing distance from an oil rig; (2) differences in phytal meiofaunal community composition with increasing macroalgal complexity; and (3) changes in average community composition of free-living nematodes along a long-term heavy metal gradient. Incorporating knowledge of an ordering structure is seen to provide more focussed, and thus stronger, ANOSIM tests, but inevitably risks losing power if that prior knowledge is incorrect or inappropriate

Item Type: Publication - Article
Additional Keywords: hypothesis test, mantel test, multivariate analysis, ordered factors, seriation
Divisions: Plymouth Marine Laboratory > National Capability categories > Single Centre NC - CLASS
Plymouth Marine Laboratory > Science Areas > Marine Ecology and Biodiversity
Depositing User: S Hawkins
Date made live: 17 Jun 2021 12:05
Last Modified: 29 Oct 2021 07:19
URI: http://plymsea.ac.uk/id/eprint/9239

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