# [R] test of CA axis

Kris Lockyear k.lockyear at ucl.ac.uk
Thu Jul 5 20:02:51 CEST 2007

Dear All,

I am not a statistician, and was wondering if anyone could help me
with the following.

Greenacre, in his Correspondence Analysis in Practice (1993, p.173)
gives a method for testing the significance of an axis in CA where:

$\chi^2 = \lambda \times n$ where \lambda is the the eigenvalue for
the principal axis and n is the number of objects in the
analysis.  The value for \chi^2 is then compared to a table of
critical values.  The table in his book is a subset of Table 51 in
Pearson and Hartley 1976, Biometrica Tables for Statisticians vol II,
described as "Percentage points of the extreme roots of
$|\text{\textbf{S}}\Sigma^{-1}-c\text{\textbf{I}}|=0$"

Is there an easy way of doing this test in R?  My main problem in
that Table 51 only gives values for a maximum of a p=10, \nu = 200
table and mine are regularly much bigger than that (although it would
be also nice to be able to put in the figures for lambda, n, p and
\nu and get the probability back).

Many thanks in advance, Kris Lockyear.

Dr Kris Lockyear
Institute of Archaeology
31-34 Gordon Square
London

phone: 020 7679 4568
email: k.lockyear at ucl.ac.uk