anderson-darling test

[Paul Kienzle]

A question for the stats gurus in the audience:

When testing rand/randn I came across a description of
the Anderson-Darling (AD) statistic for testing normality for
a set of data.  There is no simple closed form solution
for the AD CDF, but I was able to find the critical values for
p=[.1 .05 .025 .01] listed a couple of places on the web
along with a small-n correction (citing [2]). I implemented this
in octave-forge/main/stats/anderson_darling_test.m

Later, I found a paper by Marsaglia[1] giving a closed
form 6-digit approximation to the AD CDF.  I implemented
this as octave-forge/main/stats/anderson_darling_cdf.m.

The problem is that Marsaglia's values are 3x the values
I find elsewhere.

I threw a bunch of randomly generated data at Marsaglia's CDF
and it seems to give reasonable  results.  That is, for 10000
randomly generated distributions the histogram of the p-values
calculated from the Marsaglia's CDF is  approximately flat.  That
means that, e.g., the critical  value corresponding to a p-value
of .9 really is above about  90% of the AD values for random
selections from the  distribution, which is what I would expect
from a test statistic.

Anyone care to inform me what I'm doing wrong?

Thanks,

- Paul

[1] Marsaglia, G; Marsaglia JCW; (2004) "Evaluating the Anderson Darling
distribution", Journal of Statistical Software, 9(2).

[2] D'Agostino  and Stephens, Goodness-Of-Fit Techniques,
Marcel-Dekker, New York, 1986,  Table 4.7, p.123.



-------------------------------------------------------------
Octave is freely available under the terms of the GNU GPL.

Octave's home on the web:  http://www.octave.org
How to fund new projects:  http://www.octave.org/funding.html
Subscription information:  http://www.octave.org/archive.html
-------------------------------------------------------------