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# Re: st: Testing for differences in skewness and kurtosis?

 From David Hoaglin To statalist@hsphsun2.harvard.edu Subject Re: st: Testing for differences in skewness and kurtosis? Date Sat, 5 May 2012 17:10:12 -0400

```George,

Please say more about why you are interested in skewness and kurtosis.
One usually learns more about the shape of distributions by using
quantiles than by using measures based on moments, though a sample
size of 150 is a bit small to get much hold on distribution shape.

I second Nick's suggestion to use -qqplot-.  You can check on
approximate normality by plotting the quantiles of a sample against
the corresponding quantiles of the standard normal distribution.

If the two sample sizes are the same, you can plot the ordered
observations of one sample against the ordered observations of the
other sample.  And if the sample sizes aren't the same, pair up
corresponding quantiles.  If the underlying distributions have the
same shape (which need not be normal), the plot should resemble a
straight line.  Its slope will reflect the relative scale in the two
samples.  Since your standard deviations are the same, you should see
a slope around 1.

If the underlying distributions do not have the same shape, it's not
clear what equal skewness or equal kurtosis (using the moment-based
measures) would mean.  In that situation, the Q-Q plot would be
especially useful.

David Hoaglin

On Sat, May 5, 2012 at 10:34 AM, George Murray
<george.murray16@gmail.com> wrote:
> Dear Statalist,
>
> I am currently working with a very simple dataset, with two variables,
> V0 and V1 (around 150 obs each), each normally distributed, and the
> difference of the means of the distribution of the variables are
> (statistically) different, but the standard deviations are equal. I
> would like to test whether there exists any significant difference in
> the skewness of these two variables. Can this be done through
> hypothesis testing, or is this only possible through some simulation
> technique (bootstrapping?) Is there a test that is robust to the
> aforementioned conditions? Is there an equivalent test for kurtosis?
> Is anyone aware of how this can be calculated with Stata? (And no, I
> am not trying to test whether they come from the same distribution)
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