On Thu, 17 May 2001 02:33:54 +0000 (UTC), [EMAIL PROTECTED]
(rpking) wrote:
[ snip, some of my response and his old and new comments.]
> I use bootstrap to get the confidence intervals for A and B because
> they are both >0 by construction, so the exact distributions of A and
> B cannot be normal, and thus starndard distribution theory cannot
> be used to obtain CIs.
Occasionally, someone will say, as a point of theoretical interest,
such-and-so cannot be 'normal' because it has a limited range
(above zero, say).
That is, in the context I think of, a hyper-technical point being
made. It is to counter some silliness, where someone wants to
work from Perfect Normality.
Now, you have come up with the opposite silliness, and you claim
that normal distribution theory cannot be used for CIs, with that
thin excuse.
You might consider: the name of 'normal' was attached because
of the success in describing sociological data with that shape:
measures including height, weight, number of births and deaths.
Almost none of them included negative numbers.
>
> Now I want to test the null hypothesis that A - B=0. Let D=A-B. Could
> D have a normal distribution? I don't know, and that's why I'm asking.
>
As I suggested - if we are not happy with the normality of variances,
it is usually fine after we take the log. Ratios are another thing
that are usually dealt with by taking the log.
I posted:
> > ... and that is relevant to what? Distributions of raw data are
> >seldom (if ever) "asymptotically normal".
I could clarify: samples do not become 'more normal' when
the N gets larger. We hope that their *means* become better
behaved, and they usually do. They don't have to be normal
for the means to be used with the usual parametric statistics.
SO I will say, one more time, try to apply ordinary (normal)
statistics.
>
> So no social scientist should ever use asymptotic theory in their
> anaysis of (raw) data? This is certainly a very extreme view.
?? I don't know what you attributing to me -- I was trying to tell
you firmly, without being too rude, that only an ignorant amateur
will start out with bootstrapping, and will refuse to use normal
theory (like you are doing). I think you are mis-construing
'asymptotic' if you think it applies to raw data.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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