The greatest root distribution occurs everywhere in classical multivariate
analysis, but even under the null hypothesis the exact distribution has
required extensive tables or special purpose software. We describe a simple
approximation, based on the Tracy--Widom distribution, that in many cases can
be used instead of tables or software, at least for initial screening. The
quality of approximation is studied, and its use illustrated in a variety of
setttings.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS220 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org