You haven't said anything about your audience/readership. I (for one!)
would have different recommendations for a report intended for general
public consumption (e.g., parents of schoolchildren) vs. a technical
report aimed at statistical experts of one stripe or another. (For the
former, skewness and kurtosis would indeed be overkill, as you suggest;
and even for the latter, it is not clear to me that those values convey
much useful information, possibly apart from suggesting the degree to
which the distribution(s) in question depart from "normality" (aka a
Gaussian distributional model).)
Your query suggests that your readership would want to compare (or that
you think they'd want to compare, which may not be the same thing!) the
two measures of dispersion: SD and (say) semi-interquartile range.
But I rather suspect that anyone interested in such a comparison would
be sufficiently knowledgeable about matters statistical to realize that
those values are not strictly comparable (one wouldn't expect them to be
equal, for example); and reporting some non-standard measure(s) like
16th and 84th percentiles would only confuse the issue.
To answer your question, I'd recommend one-line box-&-whisker plots
(especially if you're displaying anything in graphical form), or
equivalently five-number summaries (extremes, quartiles, median in their
order of magnitude). But this is a sort of out-of-the-blue answer, and
does not take into account any characteristics either of your
audience(s) or of your reasons for wanting to report dispersions (apart,
perhaps, from a sense of clerical completeness...).
On Fri, 28 Feb 2003, John Poole wrote (edited):
> In a long list of measures (all in the same units), I report both the
> Mean and the Median: some of the measures have a skewed distribution
> and others do not ... To index the dispersion of each measure, I am
> using the Standard Deviation [with] the Mean) but am wondering what is
> best to use in relation to the Median.
< snip, discussion of alternatives >
>
> Some articles report Minimum and Maximum values of measures. <snip>
>
> At the opposite extreme, some articles list the inter-quartile range
> (values at the 25th and 75th percentile). <snip>
> However, it has the disadvantage of being narrower than the range
> defined by +/- 1 SD, making it hard to compare the dispersion of
> different measures.
>
> Do people sometimes report the Median with the 16th and 84th
> percentile (the middle 68% of the sample)? If so, what is it called?
> This range would appear to have the advantage of being directly
> comparable to the breadth of the Mean +/- 1 SD. It seems logical to
> me, but I have never seen it.
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