I have two samples. From looking at their densities, one appears symmetrical and the other from some right-tailed distribution. I would like to test that the two do not have the same skewness (ignoring issues of selective inference here).

My plan is to take a bootstrap replicates of the two samples, calculate the difference in their skewness, and repeat B times to see if a 97.5% of the values will be of one of the two sides of 0.

My questions are:

- If I were to assume normality (or make some other assumption), is there a known test for comparing the skewness of the two observations?
- Is there something I should be aware of (that I didn’t mention in my description above) when making this type of bootstrap hypothesis test?
(p.s.: examples in R are always welcome)

**Answer**

Normally you can compare the distribution of data with some exploratory analysis,(i.e if you produce boxplots) or statistical wise looking at where your mean, median and percentiles are to get a feel of your distributions. Besides that there are some tests that shows if the equality of variances can be assumed or not where comparing two or more groups.. such as Kolmogorovâ€“Smirnov test.. for this you need a non-significant result, that is the two distributions are not significantly different from one another.

**Attribution***Source : Link , Question Author : Tal Galili , Answer Author : RomRom*