Most recently, and citing earlier posts, on Fri, 12 Nov 1999 11:46:16 +0100, Markus Quandt <[EMAIL PROTECTED]> wrote: > ... > But please consider my comments to your suggestions below, and tell me > what I'm missing here... > > Rich Ulrich schrieb: > > > > On Thu, 11 Nov 1999 11:46:42 +0100, Markus Quandt > > <[EMAIL PROTECTED]> wrote: > > ... > > > we are (urgently, of course) looking for any hints on how to assess > > > significance with measures of concentration, inequality or entropy > > > (think of the Herfindahl index or Theil's measure of entropy). > > > - okay, those are unusual measures, which I don't know about. Then I went on to cite more specific questions from Marcus, which seemed to have answers that were more conventional; and which I tried to answer. I don't know anything about those measures of concentration, but that is what the question now seems to require. < snip > > As I understand it, the chi-sq. or likelihood tests will assess > differences in the distributions. That's fine with me, as long as that > difference in the shapes of two distributions goes along with a > difference in *concentration* as a property of these distributions. This <...> > But now let's say we have two observed distributions: > > 1. Distr. 2. Distr. > > Cat. Freq. Freq. > > A 20 60 > B 20 20 > C 60 20 > > Those distr. will most probably (:-)) be diagnosed as different by > chi-sq./log-likel. testing, but they have the same degree of > concentration or homogeneiety, and it is the latter concept we are > interested in. > Now, I'm not well versed in log-linear models and setting up partitions > etc. How would I go about in setting a log-linear model that allows me > to test differences in concentration? What I can offer is the comment that, so far as I have ever seen, "That is not what you test in Log-linear models." If someone has figured how to do that, that would be exceedingly clever; I would like to see it. Is this an application in communication/information theory? -- check those sources. Posting to sci.stat.math or another group might also be useful. The question was posted to sci.stat.edu and sci.stat.consult, which are groups that tend to have questions from biostatistics and the social sciences. The only examples that I have seen where "concentration" was used as a sociological variable were totally unconvincing. For instance, political organization in Italy (say) was presented as much more democratic than US, since there were numerous small parties instead of two big ones. Or maybe that was, "less democratic" -- there was no reason stated, for claiming the direction. -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html
