From: WLTPIRIE@VTVM1.BITNET (Walt Pirie)
Newsgroups: bit.listserv.stat-l
Subject: Chi-Squares
Date: 8 Nov 92 22:06:37 GMT
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU

A note of caution on the comment below:

Subtracting chi-squares to get a resultant chi-square difference
requires more than that the originals are for different models
on the same data set. For example, if the original two are
"nested" models in a log-linear  analysis, and the chi-squares
are likelihood ratio chi-squares, then it will work. If the
models are not nested, then it won't, and even if they are, if
Pearson chi-squares are used, it won't work even then.
What is being invoked in that argument is that the sum of two
chi-squares is again chi-square, but that is only valid if the
two being summed are independent.
The original inquiry did not give any information about models
or data sets, so there's no way to know. But if the chi-squares
were for different data sets, then they would be independent.
My guess is that was the case. Would their difference then be
chi-square? That would be true if it were independent of the
one being subtracted, but I suspect that would not be true.
I still feel the most important point on the original inquiry
is one raised by someone a few days ago, I don't remember who.
These were approximate chi-squares for frequency data, and as such
are approximations for which exact p-values so far out in the
tails are neither meaningful, nor comparable for different degrees
of freedom.
Walt Pirie



I sent a version of my comment on the Chi-Square probability question
privately, but the direction of the public thread leads me to post
my point to the list.

The original question dealt with how to determine which of various
Chi-Square results were "more significant" when the probability
levels associated with the statistics were all in the form .0000
The Chi-Square values were all present, but the probabilities were
indistinguishable.

I can't recall the original wording of the request, but my impression
was that the various Chi-Square values, each of which had different
degrees of freedom, were associated with various models tested on
the same data set.  If that impression is correct, then differences
among the Chi-Square values can be tested simply by subtracting the
Chi Square values and evaluating the resulting difference on the
degrees of freedom that result from substracting the larger
degrees of freedom from the smaller degrees of freedom..

Of course, if the different Chi Square values do not reflect
different models attempted on the same data, then none of the
above applies.

Dr. Francis C. Dane, Associate Professor and Chair
Department of Psychology, Mercer University
Macon, GA  31207-0001  USA
Bitnet: FDANE@UGA   Internet: FDANE@UGA.CC.UGA.EDU
Tel: (912) 752-2972
Fax: (912) 752-2108

|==================================|============================|
|  Walter R. Pirie                 |                            |
|  Department of Statistics        |                            |
|  Virginia Tech                   |                            |
|  Blacksburg, VA 24061-0439       |                            |
|                                  |                            |
|  Tel. 703-231-5441               |                            |
|  Bitnet WLTPIRIE@VTFVM1          |                            |
|  Telnet WLTPIRIE@VTVM1.CC.VT.EDU |                            |
|                                  |                            |
|  Fax  703-231-3863               |                            |
|==================================|============================|
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU