# Skewness - Interpretation

I was searching for a practical interpretation for values of skewness and I found this: https://brownmath.com/stat/shape.htm

In the interpretation it is stated - following Bulmer (1979) - that: "If skewness is less than −1 or greater than +1, the distribution is highly skewed. If skewness is between −1 and −½ or between +½ and +1, the distribution is moderately skewed. If skewness is between −½ and +½, the distribution is approximately symmetric."

Is this still valid or is there a more recent interpretation in statistics because the one from 1979 is pretty old.

p. s. I'm using Eviews to compute the skewness. The formula is: $$S=\frac {1}N \frac {\sum_{i=1}^N k^2 (y_i -y)} {\sigma^2}$$
with $y$ as the mean and $\sigma^2$ as the standard deviation.

• Depends on what measure of skewness you are using; the moment measure and the Bowley's measure based on quartiles are the popular measures which have separate ranges of variation and corresponding interpretation. Sep 26 '17 at 7:17
• I edited my post.
– PAS
Sep 26 '17 at 7:39
• Should your formula have $k^2(y_i - \bar y)^3$ in the sum? And should the denominator be $\sigma^3$? Sep 26 '17 at 16:07
• can you provide a link to the formula you gave? Sep 26 '17 at 22:46

Your formula doesn't seem to make sense to me as it stands. This Eviews page gives the following formula for skewness:

$S = \frac{1}{N} \sum_{i=1}^N \left( \frac{y_i-\bar{y}}{\hat{\sigma}}\right)^3$

where $\hat{\sigma}=s\sqrt{(N-1)/N}$

which is a fairly typical example of the various sample versions, and quite similar to the versions given at your brownmath link. I'll answer assuming that the Eviews definition I could find and the definitions given at your first link are what you intend to ask about.

I don't think perceptions of skewness have changed all that much in the last hundred years, let alone the last 40.

However, no matter what year they're made in, such prescriptions are purely a matter of opinion! There's not really any mathematical basis nor even very solid convention. Some books (including quite recent ones) contain a prescription like that but many more don't really offer an attempt at such a classification.

Personally I don't happen to agree with the prescription. In respect of the usual third-moment based skewness, if I was to put a label on it at all, to me $+1$ is in the middle of the range of fairly moderately skew, not at the boundary of "highly skew", but perhaps I've seen a lot more very skewed distributions.

Skewness is a relatively slippery concept and you have to exercise some caution in interpreting the various measures of it.

• You are totally right. I made a mistake in the formula above and thank you for your thoughts on the values and the interpretation of them.
– PAS
Sep 29 '17 at 15:43