Re: Statistical Ranking for Non-Normal Populations

From: George Kahrimanis (anakreon_at_hol.gr)
Date: 10/15/04 

Date: 15 Oct 2004 00:27:48 -0700

On 13 Oct 2004 18:30:39 +0000 (UTC) (Peter Hach) wrote:
> I need to perform (statistical) ranking of a number of large,
> but finite popolations [...] in a scenario where
> acquiring each x[i][j] is very expensive.

Richard Ulrich <Rich.Ulrich@comcast.net> replied in message
news:<uscum018tamadord3qfu63g7e5ctu7j3mr@4ax.com>...

> [...] If this is something real, there are probably a number of
> helpful conditions that could be assumed, [...]

Even if it is so, at least the "know nothing" assumption is
of considerable academic interest. It also seems to be a very good
approximation in cases of vague knowledge; think of the first researchers
in some field. Actually the first researchers have reason to mistrust
their own preconceptions, so the "know nothing" assumption is just
the right thing. We may go into examples, but I am not sure that this
discussion group is the right forum.

> But when you allow arbitrary and varied distributions,
> you don't have much chance of placing much confidence
> in the observed ordering, based on a part-sample.

A closely related question, I suppose, is "what is the use of
fussing about small samples, since *only* in the long run do we
develop a significant degree of assurance". I confess that I
used to speak like that. Now I see that unless we can say something
definite and conceptually unproblematic for small-sample inference,
there is no foundation for large-sample inference.

> [...] I think you might be stuck with generalizing
> from very gross inequalities, based on observed
> variances. Or you could have even less precision, using ranks.

I do not think that ranks give less precision than very gross
inequalities, unless the latter are based on special assumptions
(and then they would not be part of this game). A plain example, if
you have one, would be helpful.

"Ranks" names the method I used in my two previous messages. I would not
think of it as worse than "gross". (Ftm, I expect that it converges to
the prediction issued with normal approximation, but I have not
actually checked it.) If this method encompass the naked truth, we
*should* face it. Avoiding it is like believing in Santa Clauss,
because it makes us feel better (and "btw" it sells toys). (This is not
a *personal* offense, of course.)

~ George Kahrimanis

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