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Re: Usefulness of chisqr.gof

To: John Fennick <jhf2@adelphia.net>
Subject: Re: Usefulness of chisqr.gof
From: David Parkhurst <parkhurs@ariel.ucs.indiana.edu>
Date: Fri, 25 Feb 2005 09:32:31 -0500
Cc: S-News List <s-news@lists.biostat.wustl.edu>
In-reply-to: <6.2.1.2.0.20050224214658.03021f50@mail.adelphia.net>
References: <6.2.1.2.0.20050224214658.03021f50@mail.adelphia.net>
User-agent: Mozilla Thunderbird 0.7.3 (Windows/20040803)
Why bother? Great question. I call them "badness of fit tests" because they can only either establish badness, or fail to establish badness. That is the nature of significance tests. And they don't provide any measure of whether the fit is "good enough" for your purposes. They only tell you how often you would expect to get a fit as bad or worse than you got, if the true model were correct (given your sample size). Why is that useful?

I like to use qqplots for my real situation, and to compare them with a set of maybe 10--20 similar plots with the same sample size, generated from the assumption that the fit is good. That provides a benchmark.

David Parkhurst

John Fennick wrote:
Hi Group,

This is not strictly an S-plus question but, a while ago there was a thread with much discussion of the chisqr.gof test.

My experience with the test is mostly negative so I have given up on it (as well as the ks.gof). A qq plot is, to me, much more satisfying as the attachment demonstrates. The plots were not "hand-picked" they are simply 6 successive passes of the calls:

 > z<-(rnorm(500))
 > res <- rnd(chisq.gof(z)$p.va,3)
 > QQplot(z,xlab=paste('Chisq.gof = ',res,sep=''),ylab='rnorm 500')

where QQplot simply adds an lsfit to a qqplot call.

I get similar results with sizes other than 500, eg, 200, or 50000.

So, my question is, why bother with those tests?

john


John Fennick
jhf2@adelphia.net
alt: j.fennick@ieee.org
Tel: 603.526.4023
134 Brookside Drive
New London, NH 03257
USA


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