Canonical correspondence analysis is correspondence analysis constrained by a second set of measured variables. Magic Stat runs it from a species table and an environmental table, and reports the constrained inertia and a permutation p-value.
Canonical correspondence analysis is CA with a constraint: instead of finding the axes that describe the species table, it finds the axes of the species table that are linear combinations of the environmental variables. The species table is analysed on the chi-square metric, so it must be non-negative counts.
The name collides with canonical correlation analysis, which is a different method entirely. CCA here is an ordination of a species-by-sites table under a measured gradient; canonical correlation is a symmetric analysis of two blocks of continuous variables. Magic Stat runs both, under separate names, and these pages keep them apart on purpose.
The outputs that matter are the constrained inertia and its share of the total, the site and species scores, the environmental arrows in the biplot, and the permutation p-value for the overall constraint. CCA assumes unimodal responses of species to the gradient.
If your species respond linearly — a short gradient — RDA is the more appropriate constraint. If you have no environmental variables, plain CA or DCA is what you want.
Two matrices: X (non-negative species or response table) and Y (environmental variables), matched by row. Negative values in X are rejected with a pointer to the chi-square transformation.
Transformations available in the dialog: None · Z-score (standardise) · ln(1+x) · ln(x) · Hellinger · Chord · Chi-square · Square root · Range 0–1. For a raw count table, None keeps the chi-square metric the method is built on.
CCA assumes unimodal species responses, which is typical of long environmental gradients; RDA assumes linear responses and is the safer choice on short gradients. The gradient length from a DCA, if you run one, is the usual way to decide.
Different methods with overlapping names. Canonical correspondence analysis is a constrained ordination of a species table by environmental variables. Canonical correlation is a symmetric analysis of two blocks of continuous variables, with no response-and-explanation split. Use the one that matches your design.
It permutes the environmental rows to build a null distribution for the overall constraint, using the dialog's standard number of permutations. If you need tests by axis or by term, partial CCA, or a specific permutation design with blocks or strata, vegan in R is the appropriate tool — we would rather point you there than overstate this one.
Often the raw counts are fine, because the chi-square metric is internal to CCA. If you do transform, state which transformation you used; applying a chi-square transformation on top of a chi-square method needs to be a deliberate choice.
No. Everything runs on your machine. The only automatic signal is an anonymous installation counter.
Redundancy analysis → Correspondence analysis → Canonical correlation →