# Permutation test to test significance of skewness/kurtosis of two distributions?

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.

• I think this would work to test whether one distribution is significantly more skew than another. – Peter Flom - Reinstate Monica Oct 10 '12 at 23:07