Welch-type PERMANOVA robust to unequal dispersion

Tests whether community composition differs among groups with the W*d statistic of Hamidi et al. (2019), a distance-based generalisation of Welch's ANOVA. Unlike classic PERMANOVA (beta_permanova()), it does not assume that groups have the same multivariate dispersion, so a significant result reflects a shift in location even when groups differ in spread or size. For two groups it equals the Tw2 test of Alekseyenko (2016). With one variable and Euclidean distance it equals Welch's F statistic (stats::oneway.test() with var.equal = FALSE).

Usage

beta_welch(
  data,
  site = site,
  species = species,
  abundance = NULL,
  group,
  env = NULL,
  distance = "bray",
  transform = "none",
  permutations = 999
)

Arguments

data

A data frame in long format, with one row per record.

site, species

<tidy-select> The column holding site identifiers and the column holding species names.

abundance

<tidy-select> The column holding counts. If NULL (the default), a column called abundance is used when present, otherwise every row counts as one individual.

group

Site variable (unquoted) defining the groups.

env

A data frame of site variables with a column named like the site column. By default, site variables are taken from data: every column that is constant within each site.

distance

Dissimilarity for "pcoa", "nmds" and "dbrda", passed to vegan::vegdist(), such as "bray" (the default) or "jaccard".

transform

Transformation of the community matrix before the analysis: "hellinger" (the default for PCA and RDA, which otherwise overweight abundant species; Legendre and Gallagher 2001), "chord", "log" (log(x) + 1 for x > 0), "sqrt", "pa" (presence-absence) or "none" (the default for the other methods).

permutations

Number of permutations.

Value

A one-row tibble with statistic (W*d), n_groups, n_sites and p.value.

Details

The p-value is obtained by permuting group labels.

References

Hamidi, B. et al. (2019). W*d-test: robust distance-based multivariate analysis of variance. Microbiome, 7, 51. doi:10.1186/s40168-019-0659-9

Alekseyenko, A. V. (2016). Multivariate Welch t-test on distances. Bioinformatics, 32, 3552-3558. doi:10.1093/bioinformatics/btw524

Examples

ants <- dplyr::mutate(png_ants, unit = paste(site, season, transect))
set.seed(1)
beta_welch(ants, site = unit, group = season, permutations = 199)
#> # A tibble: 1 x 4
#>   statistic n_groups n_sites p.value
#>       <dbl>    <int>   <int>   <dbl>
#> 1      1.29        2      20   0.165