---

name: statistics-ordination description: "Run scikit-bio distance-matrix statistics, ordination, compositional analyses, and biological embedding summaries." disable-model-invocation: true metadata: disco-role: operating license: BSD 3-Clause

statistics-ordination

Use this sub-skill when a task asks to test group differences from a scikit-bio DistanceMatrix, compare distance matrices, run ordination, transform or test compositional data, or convert biological embedding vectors into distances, ordination, or tabular summaries.

Read First

• references/api-reference.md for public signatures, return objects, accepted input shapes, and result fields.
• references/workflows.md for copy-ready patterns covering distance tests, metadata alignment, ordination, composition transforms, ANCOM-style tests, and embeddings.
• references/troubleshooting.md for matrix validity, ID mismatches, permutation reproducibility, PCoA warnings, compositional zeros, differential-abundance shape issues, and backend limits.
• scripts/stats_ordination_smoke.py for a deterministic smoke check covering DistanceMatrix, permanova, pcoa, composition zero handling, and ProteinVector embedding utilities.

Route Here For

• Constructing or validating PairwiseMatrix, SymmetricMatrix, DistanceMatrix, and random distance matrices with randdm.
• Running permanova, anosim, permdisp, mantel, pwmantel, or bioenv on existing distance matrices and aligned metadata.
• Running pcoa, pcoa_biplot, ca, cca, rda, mmvec, or inspecting OrdinationResults fields.
• Applying closure, multi_replace, clr, ilr, alr, rclr, ANCOM, ANCOM-BC, structural-zero checks, or Dirichlet-multinomial differential-abundance tests.
• Creating SequenceEmbedding, ProteinVector, or related embedding vectors and converting them with embed_vec_to_distances, embed_vec_to_ordination, embed_vec_to_dataframe, or embed_vec_to_numpy.

Boundaries

• For count-matrix generation, alpha/beta diversity computation, BIOM-style table preparation, and sample-by-feature orientation repairs, use ../diversity-tables/SKILL.md first and return here once distances, compositions, or table-like inputs exist.
• For metadata file loading, ID normalization from external formats, or I/O registry details, use ../io-metadata/SKILL.md before running statistics.
• For tree construction, rooting, tree-based basis construction, or phylogenetic interpretation, use ../trees-phylogeny/SKILL.md.
• Keep this sub-skill focused on statistical analyses, ordination outputs, compositional transforms/tests, embedding summaries, and their diagnostics.

Public Smoke Check

Run the bundled script from any working directory after installing scikit-bio:

python scripts/stats_ordination_smoke.py
python scripts/stats_ordination_smoke.py --permutations 9 --seed 7
python scripts/stats_ordination_smoke.py --help

The script imports public scikit-bio APIs only, constructs a small DistanceMatrix, runs PERMANOVA and PCoA, applies zero replacement before CLR, creates simple ProteinVector objects, and prints compact JSON.