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To test the significance of the skewness difference between two distributions with $N_1$ and $N_2$ samples, would the following test work:

  1. Create a single array of all the samples from both distributions.

  2. Randomly shuffle the array .

  3. Split the array at index $N_1$.

  4. Calculate the $abs()$ of difference of the skewness/kurtosis statistics for the two partitions.

  5. Repeat until desired precision/out of unique permutations.

Then check if the actual $abs()$ difference of skewness/kurtosis statistics lie beyond the $p = 0.05$ interval.

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    $\begingroup$ I think this would work to test whether one distribution is significantly more skew than another. $\endgroup$ – Peter Flom - Reinstate Monica Oct 10 '12 at 23:07
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Yes, this method is correct, assuming you do not care about the direction of the difference.

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