Re: optimal sample size
On Mon, 1 Oct 2001 21:52:08 +0200, "Bernhard Kuster" <[EMAIL PROTECTED]> wrote: [me] > > > I think I am trying to say, gently, that your basic question doesn't > > make very good sense to me; and it did not, to Dennis, either. > > "Optimal" is one problematic word. Another problem is that > > you seem to ask about all research, in all of the world > > It might be a clever way to attack 'sample size', but I think > > that hasn't been done. BK > > Thanks for your advise. I see that the question is probably a little bit > overloaded and that optimal is not a good definition. But isn't there > something that determines the sample size of all statistical techniques? I > remember having read something a long time ago, that sample size of all > statistical techniques are influenced by alpha risk, power and effect size. > Is this wrong or is not applicable to my question? "Influenced" is an inadequate word. And there is nothing to be "optimal" when the relations are 1-to-1. Once you have your choice of parameterization, there is a strict, 5-dimensional relation. Here is one way to describe it: " a) for a given test b) if there is a specific, assumed N c) and (standardized) effect size, then: d) using a given alpha (risk, one or two tailed) e) will give you a test with power ... (or 1.0 minus beta-error) [that can be determined as follows ]" Saying it in another way: (Almost always) there is a trade-off between beta and alpha (type 2 and type 1 errors). For ANOVA, the factors (b) and (c), above, can be encompassed in the "non-centrality parameter", which is the product of N times distance-squared. (Actually, that is Degrees of freedom instead of N.) A given "noncentrality" has a specific set of alpha and beta values that can be computed, where the one error can be traded-off against the other. The articles and books that get written are about parameterizations that are useful, or trade-offs that are recommended. Or designs that are efficient. These vary by area -- Jacob Cohen wrote the book that is most used in "behavioral science" (from its title) and clinical research. The book is not concerned with designed N's of over 1000, or N's under 10; and it has a very particular orientation towards designs in that middle range, stating a judgement on what effects are small, medium or large. Okay, he was describing the world that a lot of us work in. But it is certainly not the only sort of research that exists. As I read it in your earlier message, you were asking about "an expert" who -- I think -- would be like an expert in doing long division. Not necessary. Not a good idea. That is: no one has asked for scientific proof on that level, for a few hundred years. A lot of people know what "statistical power" is, and there is no controversy as to shape of the general topic. So you need a more specific question. -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: optimal sample size
> I think I am trying to say, gently, that your basic question doesn't > make very good sense to me; and it did not, to Dennis, either. > "Optimal" is one problematic word. Another problem is that > you seem to ask about all research, in all of the world > It might be a clever way to attack 'sample size', but I think > that hasn't been done. Thanks for your advise. I see that the question is probably a little bit overloaded and that optimal is not a good definition. But isn't there something that determines the sample size of all statistical techniques? I remember having read something a long time ago, that sample size of all statistical techniques are influenced by alpha risk, power and effect size. Is this wrong or is not applicable to my question? = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: optimal sample size
> what is the MINIMAL n needed to accomplish these ends" ... that might be optimal if you are looking for the > smallest n you can get by with ... but, optimal does not have to be defined > as such ... Thanks for your comments. To be honest, for me the term "opitmal" (which seems not to be a very good term) reffered completely to the task of minimizing sample size without risking to not be able to reject the "null hypothesis". What could be another definition of optimal in connection with sample size? = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: optimal sample size
On Mon, 1 Oct 2001 12:23:28 +0200, "Bernhard Kuster"
<[EMAIL PROTECTED]> wrote:
> Hi
>
> I am interessted in the question of optimal sample size in general, not for
> a special statistical technique.
(a) There was a notable 1974 article on "Believability when N=1" and
here is an academic webpage on the subject. It includes good
references.
http://www-personal.umich.edu/~hinderer/scrdoutline.html
(b) Richard Peto's writing may have been the impetus behind
one or two "mega-studies." He pointed out that by having
a clear-cut, randomized treatment ("treatment
given within x hours of a heart attack") and an unambiguous
outcome ("still alive after 30 days"), it should be possible
to combine the experience of hundreds of hospitals,
and 10,000's of patients. And it was done. I think that the
randomization was in there, and was possible because
no one had great faith in the treatment. The huge N was
a *necessary* sample size because of the small size of the
expected effect as an odds ratio, and the small fraction of
people who would be mortalities-who-might-be-saved.
There you have the extremes of what is optimum for
"sample size in general, not for a special technique."
>
> My questions: (1) What do I have to keep in mind if I compute optimal sample
> size, what is relevant? (2) What are the classic studies and who has highly
> influenced the subject? (3) What are the problems discussed right now by the
> scientific community? (4) What are the relevant journals and is there some
> information on the web?
I think you might find some issues included in Robert P. Abelson,
"Statistics as principled argument."
I think I am trying to say, gently, that your basic question doesn't
make very good sense to me; and it did not, to Dennis, either.
"Optimal" is one problematic word. Another problem is that
you seem to ask about all research, in all of the world
It might be a clever way to attack 'sample size', but I think
that hasn't been done.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
=
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
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Re: optimal sample size
of course. the most important issue is ... what do you mean by optimal? if you can specify what the purpose of the sampling project is ... the parameter to be estimated, within what margin of error, etc. ... then you might be able to answer the question ... "what is the MINIMAL n needed to accomplish these ends" ... that might be optimal if you are looking for the smallest n you can get by with ... but, optimal does not have to be defined as such ... At 12:23 PM 10/1/01 +0200, Bernhard Kuster wrote: >Hi > >I am interessted in the question of optimal sample size in general, not for >a special statistical technique. > >My questions: (1) What do I have to keep in mind if I compute optimal sample >size, what is relevant? (2) What are the classic studies and who has highly >influenced the subject? (3) What are the problems discussed right now by the >scientific community? (4) What are the relevant journals and is there some >information on the web? > >Can anybody advise on one or more of these questions? Thanks a lot! > >Bernhard > > > >= >Instructions for joining and leaving this list and remarks about >the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ >= _ dennis roberts, educational psychology, penn state university 208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED] http://roberts.ed.psu.edu/users/droberts/drober~1.htm = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
