🚀 go-pugleaf

Hello.  A few days ago I asked for information about how to test whether
two unrelated samples had different variances, and received a number
of helpful pointers from folks.  I would recommend the chapter in
Hollander and Wolfe as a useful place to start, if anyone else is
interested.

From a layman's viewpoint, an important criterion seems to be how
many assumptions you are prepared to make about the distribution.
If you can't make any, Moses test seems to be indicated.  If you're
happy to make some (asymptotic) assumptions, then Miller's jacknife
seems useful.  Unfortunately, the tests mentioned by Hollander and
Wolfe are not implemented in most of the standard packages.

Since my own data seems to be near normally distributed (both
on a priori and a posteriori grounds), I thought I might 
persevere with the traditional F test for variances, even though
this is known to be very sensitive to non-normality.  In particular,
I have been looking at Box and Andersen's adjustment to this test
(JRSS, B, 1955, v 17, p1-26).  They adjust the degrees of freedom of
the traditional F test for variances by a factor which depends on the
normality of the distribution.  I'ld like to make this adjustment to
my own data, but, as a non-statistician, I'm having a bit of trouble
understanding their notation.  They give the modfication factor
to the degrees of freedom as (1 + 1/2*gamma_2)^-1 (their equation 48,
on p. 17).  My question: what is gamma_2?  It looks as though it is
the kurtosis of both samples taken together, minus 3.  That certainly
fits with what Box and Andersen say later on p. 17.  Can anyone 
confirm that, or make any other relevant comments about adjusting
the degrees of freedom in such cases?

Thankyou.

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Patrick Haggard                         Email (WORLD): ph@physiol.ox.ac.uk
University Laboratory of Physiology     Email (JANET): ph@uk.ac.ox.physiol
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