>Radford Neal wrote:
>> ... the median is probably not
>> the best thing to look at, whatever you might have been taught. What
>> to look at depends not just on the shape of the distribution, but also
>> on what your purpose is. Ask yourself whether there are very many
>> purposes for which it would make no difference if the upper 49% of the
>> incomes were doubled, leaving the median unchanged.
Alan Hutson <[EMAIL PROTECTED]> wrote:
>Yes, the median may not change, but the confidence interval and/or
>the variance estimate for the median will reflect the fact that
>something is different in the upper tail. Also, in your
>hypothetical above you are assuming one would estimate the median
>with "middle" order statistic.
My point is not anything to do with problems of estimating the median,
but rather with whether you should be interested in the median at all.
Since the population median would be the same even if the upper 49% of
the values were doubled, it seems unlikely that it's what you really
are interested in. In contrast, the mean corresponds to the sort of
aggregate that is of interest in many contexts. Mean income, for
instance, will tell you something about how much money is available to
spend on goods. Of course, for many purposes, no single number will
be an adequate description of the situation.
As a technical point, a confidence interval for the median is not
necessarily going to be influenced by the upper tail. If you are
interested in the shape of the tails, you should look at them.
Radford Neal
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Radford M. Neal [EMAIL PROTECTED]
Dept. of Statistics and Dept. of Computer Science [EMAIL PROTECTED]
University of Toronto http://www.cs.utoronto.ca/~radford
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