PERMANOVA using the F2 Statistic

Implements the F2 statistic of Anderson et al. (2017) for permutational multivariate analysis of variance (PERMANOVA) on dissimilarity matrices. The F2 statistic uses group-specific dispersion estimates, so group centroids can be compared when dispersions differ and group sizes are unequal. P-values are obtained by permutation, bootstrap, or bias-adjusted bootstrap. The formula interface follows 'adonis2()' in the 'vegan' package.

F2Adonis2

F2Adonis2 is a tool for multivariate hypothesis testing, developed to support clinical metabolomics and high-dimensional omics research. It addresses the multivariate Behrens-Fisher Problem in dissimilarity-based analyses (such as PERMANOVA), providing a statistically sound approach for datasets where group dispersions are heterogeneous. It is available on GitHub.

Motivation

In high-dimensional ecological and metabolomics studies ($P \gg N$), standard PERMANOVA ($F_1$) methods often yield inflated Type I error rates when group dispersions are unequal (heteroskedasticity) and group sizes are unbalanced.

This package implements the methodological solutions proposed by Anderson et al. (2017). Rather than pooling variance across groups (which leads to bias), the $F_2$ statistic uses a weighted combination of group-specific dispersion estimates to maintain level accuracy under heteroskedastic conditions.

Installation

You must install the remotes package first.

install.packages("remotes")

Then, use install_github to install this package.

remotes::install_github("LakviruPerera/F2Adonis2")

Quick Start

F2Adonis2 acts as a drop-in replacement for vegan::adonis2. It follows the standard R formula interface and accepts either a data matrix (distances are computed with vegdist) or a precomputed dissimilarity (dist) object on the left-hand side.

library(F2Adonis2)

# Example data included with the package
data("pkd_metadata", package = "F2Adonis2")
data("pkd_metabolites", package = "F2Adonis2")

pkd_meta <- data.frame(Group = factor(pkd_metadata$Group))

# Run the F2 test (use more permutations, e.g. 999, for final results)
fit_f2 <- F2_adonis2(
  as.matrix(pkd_metabolites) ~ Group,
  data = pkd_meta,
  method = "euclidean",
  permutations = 99
)

# View results
print(fit_f2)

Testing

The package is checked with R CMD check on Linux, macOS, and Windows through GitHub Actions (see the badge above). It was also checked independently on Windows 11 (R 4.6.1) and Ubuntu 26.04 LTS (R 4.6.0) during development.

Support and contributing

Questions and bug reports are welcome on the issue tracker. See CONTRIBUTING.md for how to report a bug or propose a change.

License

GPL-2. Parts of the code are adapted from the 'vegan' package, which is also licensed under GPL-2.

References

Anderson, M.J., Walsh, D.C.I., Robert Clarke, K., Gorley, R.N. and Guerra-Castro, E. (2017), Some solutions to the multivariate Behrens–Fisher problem for dissimilarity-based analyses. Aust. N. Z. J. Stat., 59: 57-79. doi:10.1111/anzs.12176

Oksanen J, Simpson G, Blanchet F, Kindt R, Legendre P, Minchin P, O’Hara R, Solymos P, Stevens M, Szoecs E, Wagner H, Barbour M, Bedward M, Bolker B, Borcard D, Borman T, Carvalho G, Chirico M, De Caceres M, Durand S, Evangelista H, FitzJohn R, Friendly M, Furneaux B, Hannigan G, Hill M, Lahti L, Martino C, McGlinn D, Ouellette M, Ribeiro Cunha E, Smith T, Stier A, Ter Braak C, Weedon J (2026). vegan: Community Ecology Package. doi:10.32614/CRAN.package.vegan, R package version 2.7-3, https://CRAN.R-project.org/package=vegan