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

 From Nick Cox To statalist@hsphsun2.harvard.edu Subject Re: st: Testing for differences in skewness and kurtosis? Date Mon, 7 May 2012 10:05:27 +0100

```This is just to emphasise that -qqplot- automatically deals with
comparison of quantiles, regardless of whether sample sizes are
identical, or even of whether non-missing values are in the same
observations.

On Sat, May 5, 2012 at 10:10 PM, David Hoaglin <dchoaglin@gmail.com> wrote:
> 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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```