On 28 Feb 2003 at 10:13, Dennis Roberts wrote:
In addition ti what others have said on this: For a measure ov
variability of the median, twopossibilities are
1) The asymptotic variance of the median (if the sample size is
somewhat large). This asympototic variance is
the inverse of
(n/0.25) f(\eta)^2
where \eta is the median , f(\eta) is the density at the median.
This can be estimated by kernel density smoothing. (I have code
doing this in R).
2) By bootstrapping.
Kjetil Halvorsen
> At 09:59 AM 2/28/03 +0000, John Poole wrote:
> >In a lengthy list of measures (which are all in the same units), I am
> >reporting both the Mean and the Median because some of the measures
> >have a skewed distribution and others do not (I might also list the
> >skewness and kurtosis, but that may be overkill). To index the
> >dispersion of each measure, I am including the Standard Deviation
> >(which seems most relevant in relation to the Mean) but am wondering
> >what is best to use in relation to the Median.
>
> as don suggested, it is hard to know how to advise if we don't know the
> level of the audience
>
> but, as a general rule ... NONE of these summary statistics really tell you
> about the distribution so, my first question is: can you show a picture of
> the distributions ... like dotplots?
>
> if you can ... then, doing something like what minitab does with its
> describe command should be more than sufficient ... gives mean and median
> ... Q1 and Q3 ... low and hi values ... and with the actual shape shown by
> the dotplot ... what else would you need?
>
> don suggested boxplots but ... the difficulty with those is that they do
> NOT adequately show you the distributional shape and ... that seems to be
> of concern to you... and, some distributions if they are radically skewed
> ... showing a dotplot ... histogram ... or some other "graph" of the data
> would be useful ALONG with basic summary statistics ...
>
> don't worry about trying to find some variability measure that goes along
> with the median ... while the semi interquartile range is sometimes used
> ... there is nothing inherently connected between it and the median ...
>
> .
> .
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