Skewness

[Brad Lockerbie]

I am running Stata 14. The skewness statistic comes back radically different than the one I get by hand using the formula 3(Mean-Median)/standard deviation. Does Stata 14 use a different formula? If so, where can see some documentation concerning it.

[Nick Cox]

Skewness is calculated by several commands, but I think you'll find that the documentation for summarize answers your question. The skewness measure it calculates is based on moments around the mean. https://www.stata.com/manuals/rsummarize.pdf p.9 is accessible from outside Stata. The same document is bundled with your Stata as part of the pdf documentation.

Only exceptionally will this coincide with the measure you calculate. Even if moment-based skewness is exactly 0 that doesn't guarantee that mean = median, although conversely all symmetric distributions will have mean = median (and some others too).

I am not aware of any official command that calculates your measure, which Karl Pearson discussed, although various people have pointed out from time to time that it's easy enough to calculate from summarize results.

(This isn't rigorous as there are also symmetric distributions for which moments are undefined.)