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From |
Nick Cox <njcoxstata@gmail.com> |

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) > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Testing for differences in skewness and kurtosis?***From:*George Murray <george.murray16@gmail.com>

**Re: st: Testing for differences in skewness and kurtosis?***From:*David Hoaglin <dchoaglin@gmail.com>

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