Subject: Re: Mathematical methods (Was: Re: Sampling and Vulgate)

From: [email-masked] (Nichael Lynn Cramer)
Date: Wed, 1 May 1996 12:26:10 -0400

Robert B. Waltz wrote:
>On Tue, 30 Apr 96, [email-masked] (Vincent Broman)
>>If your sampling method is biased, increasing the sample size won't help,
>>the larger sample will still be biased, it just has a smaller variance.
>I must disagree with both halves of this statement. First, increasing
>the sample size DOES help, at least somewhat (to argue by analogy --
>if you take a public opinion poll, and ask 90% of the people, you
>don't have to use an unbiased sample; you will still be close. Not
>that I am claiming to sample anything like 90% of the variants).

I think, thought, that the critical phrase in the above, though, is "If
your sampling method is biased".  In the analogy of the public opinon poll
an obvious case would be if, for some reason you were only to poll
Republicans or, say, people in your immediate telephoning area (reportedly
the fallacy that was responsible for the poll that led to that wonderful
photograph of Truman holding the newspaper above his head).

The point being that either of these cases simply increasing the sample
size, under the _existing_ polling conditions, would do nothing to increase
the accuracy of the poll (excluding the trivial case of "increasing the
poll until you had polled every Republican in the country and were forced
to start including others".)

>Also, we should not mistake the meaning of variance. This is REALLY
>important, folks. I am a mathematician; I KNOW.

Yes, there are many of us here who have such training.

(In point of fact, this in itself serves as a good example of point above.
I.e. the population in question here is --because of the nature of the
medium-- _strongly_ biased towards computer and other professionals who
have had (typically much) more technical training than a comparably-sized
sample of the "population at large".   ;-)

>[...]
>>And you would have a hard time convincing me that the selection
>>of variants in the UBS3 apparatus is =independent= of the attestation
>>by texttypes.
>
>That last statement, at least, I agree with. That's the exact reason
>why I increased the sample.

But again, haven't we come full circle to the issue of manuscripts needing
to be "weighed not counted"?

The critical issue, of course, is the neccessity of demonstating the
_independence_ of the elements of the sample, otherwise it is useless to
simply increasing the total number of manuscripts.  As a trivial example,
if manuscript Y is shown to be a direct copy of manuscript X including both
has does nothing meaningful increase the sample size in the same way that,
say, were some verion shown to be tracable to a single exemplar the dozen
or perhaps hundreds of manuscripts of that version carries no more weight
than that of a single manuscript.

Nichael
[email-masked]                                               __
http://www.sover.net/~nichael              Be as passersby   -- IC