Analysis of similarities (ANOSIM) for 3‐way designs

Somerfield, PJ, Clarke, KR and Gorley, RN 2021 Analysis of similarities (ANOSIM) for 3‐way designs. Austral Ecology. 927-941.

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Analysis of similarities (ANOSIM) is a robust non-parametric hypothesis-testing framework for differences in resemblances among groups of samples. To date, the generalisation and use of ANOSIM to analyse various 2-way nested and crossed designs with unordered or ordered factors has been described. This paper describes how the 2-way tests may be extended and modified for the analysis of 3-way designs, including the introduction of a different type of constrained permutation procedure for a design in which one factor is nested in another and crossed with a third. The construction of 3-way tests using the generalised statistic in various nested and crossed designs, with or without ordered factors, and with or without replication, is described. Applications of the new tests to ecological data are demonstrated using three marine examples. They are as follows: a study of changes in fish diet for fish of increasing size sampled in different locations at different times (a 3-way fully crossed design with ordered factors); a hierarchical spatial study of the fauna inhabiting kelp holdfasts (a 3- way fully nested design with unordered factors); and a study of infaunal macrobenthos in which sites within areas were resampled over a long time series (a design in which sites are nested in areas but crossed with years, both latter factors potentially being ordered). The magnitudes of the ANOSIM statistics provide information about relative effect sizes (accounting for other factors), which is often a focus for multifactorial designs. Though the described ANOSIM tests do not provide parallels for all the range of 3-way mixed-factor designs possible in ANOVA (and its multivariate semi-parametric counterpart PERMANOVA), it is seen that for nested factors these ANOSIM tests parallel the matching PERMANOVA random-effects models, and not their fixed-effects counterparts, thus allowing the same broader inference about the space from which these random factor levels are drawn.

Item Type: Publication - Article
Additional Keywords: hypothesis tests, multifactorial designs, multivariate data, non-parametric statistics, ordered factors
Divisions: Plymouth Marine Laboratory > National Capability categories > Added Value
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: 15 Aug 2021 08:49
Last Modified: 29 Oct 2021 07:26

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