On 21 Dec 1999 08:21:05 -0800, [EMAIL PROTECTED] (Robert
Dawson) wrote:
> Ronald B. Livingston asked:
>
> >Are there "standards" for describing the skew of a distribution? For
> >example, 0 to 1 = mild; 1 - 2 = moderate, etc. I am aware of tests of
> >significance for skew, but with large samples practically any skew is
> >significant. Any references would be appreciated.
>
> One possibility would be to see what transformation (if any) would
> symmetrize the distribution (or remove its skewness, anyhow). This is not
> quite what you asked for, but might have advantages.
>
> -Robert Dawson
What Robert says here might seem like a redundancy to some people,
if they have not looked at actual data that contradicts it.
That is, it frequently does work out that "more severe
skewness implies: a stronger transformation is needed";
but it is a naive assumption, and it is wrong, if you assume that it
has to work out that way.
To normalize and create symmetry, you can have diverse amounts of
skewness that do require the same transformation, or
vice-versa: the same skewness might merit diverse transformations.
A set of data may be log-normal where the max is only 1.1 times the
minimum -- in which case, the log-normal will be barely skewed, and
hard to distinguish from normal.
[For instance, take a normal (1000, 1) and exponentiate.]
At the other extreme, if the max is 1000 times the min,
the skewness will be large and hard to ignore.
Similarly, if you square the numbers in the range of 1 to 10, you will
see much more skewness that if you square the numbers from 101 to 110.
I don't usually see as much skewness with the square as I expect with
exponentiating -- but it is possible to have parallel data sets with
equal (though not extreme) skewness. When that is the case, the data
set that wants the LOG is the one where the normal assumption is more
severely violated, so far as the robustness of the two-sample t-test,
unequal Ns, is concerned.
[I don't have a reference for that. The unsurprising conclusion is
based on unpublished monte carlo explorations that I did a few years
ago; and should not be hard to duplicate.]
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
