PCoA analysis

Principal coordinates analysis from your own data

PCoA, also called classical multidimensional scaling, answers the same visual question as NMDS — do my samples group? — but from a dissimilarity matrix and with a metric fit. In Magic Stat it is a dialog, not a script.

The honest part

PCoA, and the difference from NMDS that actually matters

PCoA takes a dissimilarity matrix between samples and places them in a low-dimensional space, trying to preserve the distances themselves rather than only their ranking. That is the practical difference from NMDS: PCoA is a metric method, so it reports how much of the variation the axes explain, while NMDS only reports stress.

It is the natural companion to any distance-based analysis — the ordination you draw next to a PERMANOVA, using the same dissimilarity measure, on the same data. If you have already chosen Bray–Curtis for one, staying with Bray–Curtis for the other is not a stylistic choice, it is what makes the two results describe the same thing.

The awkward part has always been the plumbing: computing the distance matrix, feeding it to the ordination, and getting a figure whose axes you can label without guessing.

What it does

What Magic Stat gives you for PCoA

How it works

Distance matrix to figure

  1. Load the data. the same spreadsheet you use for the rest of the analysis.
  2. Choose PCoA. Statistics → Multivariate → PCoA.
  3. Set the dissimilarity and transformation. match them to the data (Bray–Curtis and Hellinger cover most abundance work).
  4. Draw and colour. colour the samples by a categorical column so the grouping is visible in the figure.
  5. Export. figure to the gallery, report to .docx/.html/.md.
Options

The settings, in the dialog

Dissimilarity measures: Bray–Curtis · Euclidean · Manhattan · Canberra · Jaccard · Sorensen · Horn–Morisita.

Transformations: None · Z-score (standardise) · ln(1+x) · ln(x) · Hellinger · Chord · Chi-square · Square root · Range 0–1.

Frequently asked

PCoA questions, answered honestly

PCoA or NMDS?

PCoA is metric: it preserves the distances and tells you how much variation the axes explain. NMDS is non-metric: it preserves only the ranking, and reports stress. For strongly non-linear data NMDS often gives the more readable picture; for a figure that pairs with PERMANOVA, PCoA is the natural choice.

Which dissimilarity?

Match it to the data. Bray–Curtis for abundance, Jaccard or Sorensen for presence/absence, Euclidean for standardised continuous variables.

Do I need R?

No. If you use R comfortably, keep it; the value here is the output and the manuscript workflow.

Is my data uploaded somewhere?

No — the analysis runs locally. The only automatic signal is an anonymous installation counter with no data in it.

NMDS analysis → PCA analysis →