About This Calculator

This is what it does.

Compositional Statistics Calculator Description

This calculator performs computations described in A Concise Guide to Compositional Data Analysis by John Aitchison.

First, it transforms raw data (x1, x2, x3,…) into a composition (X1, X2, X3,…), whose value sum to 1, or 100%. It would also normalize a raw composition (x1, x2, x3,…)  into a unit-sum constrained composition (X1, X2, X3,…).

It then performs a logratio transformation of the composition followed by computation of distributional variation as three matrix specifications:

  1. logratio covariance matrix,
  2. centered logratio covariance matrix, and
  3. variation matrix.

Finally, it computes measures of central tendency using two algorithms which produce identical results:

  1. logratio mean vector, and
  2. centered logratio mean vector.