In article <[EMAIL PROTECTED]>,
Richard A. Beldin <[EMAIL PROTECTED]> wrote:
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>You have raised the right questions.
>Textbooks try to present theory and applications both. Sometimes they
>are focussing on theory and forget that real world applications rarely
>satisfy the assumptions. Sometimes the applications are so important, we
>are willing to extrapolate the theory beyond its range of applicability.
>>Yes, we have an interval that may contain the true population mean, but
>... if the distribution is
>>heavily skewed to the right, say like income, why do we want an
>interval for the population mean,
>>when we are taught that the median is a better measure of central
>tendency for skewed
>>distributions?
>The sampling theory for means is well understood and requires few
>assumptions.
Wrong! The APPROXIMATE large sample theory for means
is as you state; it requires a finite variance. But
the rate of convergence is not that great.
A corresponding sampling theory for medians from skewed
>distributions would require a quantitative specification of the amount
>of skewing.
On the other hand, the small sample theory for order
statistics from a continuous distribution is not at all
difficult; this is a standard exercise in beginning
theoretical courses. A good classical confidence interval
for the median would just be the interval between certain
order statistics, and this would be as claimed for all
continuous distributions.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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