Skewness statistic - how close to zero should it be? I am working my way through Chapter 3 in the Applied Predictive Modeling by Kuhn and Johnson. In section 3.2 the discussion values close to zero indicate symmetry. My question is - how close to zero? In the end of chapter exercises the preprocess function transforms some from 1.7 to .9 - is that close enough?
 A: Different references will tell you different cut-off points for skewness.
I use a cut-off of 2 for the absolute value of the skewness, so I assume that is reasonably close to zero if:
$$
-2 \leq skew \leq 2
$$

Some citations with references (some of them are incomplete, sorry). I'm sorry but I have these in some notes, but I don't have recorded which skewness formula and which kurtosis formula the authors are referring to. Following Nick Cox's comments I've added some remarks to some of the quotes.
"The values for asymmetry and kurtosis between $-2$ and $+2$ are considered acceptable in order to prove normal univariate distribution."
George, D., & Mallery, M. (2010). SPSS for Windows Step by Step: A Simple Guide and Reference, 17.0 update (10a ed.) Boston: Pearson.
In my opinion, prove normal univariate distribution should be replaced by assume a univariate distribution close to the normal in the above sentence.
"The acceptable range for skewness or kurtosis below $+1.5$ and above $-1.5$."
Tabachnick & Fidell (2013).
"Most of the researchers in the field of social science are following a less stringent [criterion] based on the suggestion by Kline (1998, 2005). Data with a skew above an absolute value of $3.0$ and kurtosis above an absolute value of $8.0$ are considered problematic."
It is possible that Kline is referring to kurtosis and not to excess kurtosis, while Tabachnick & Fidell may be referring to excess kurtosis. Even so, Kline provided the largest cut-offs that I've seen so far.
"It can be consider[ed] normal when $-1<$skewness$<1$."
Bulmer M. G. (1979), Principles of Statistics.
I would say close to the normal distribution.
"Indices for acceptable limits of $\pm 2$" (of skewness and excess kurtosis).
Trochim & Donnelly, 2006; Field, 2000 & 2009; Gravetter & Wallnau, 2014.
Trochim, W. M., & Donnelly, J. P. (2006). The research methods knowledge base (3rd ed.). Cincinnati, OH:Atomic Dog.
Gravetter, F., & Wallnau, L. (2014). Essentials of statistics for the behavioral sciences (8th ed.). Belmont, CA: Wadsworth.
Field, A. (2000). Discovering statistics using SPSS for Windows. London-Thousand Oaks- New Delhi: Sage publications.
Field, A. (2009). Discovering statistics using SPSS. London: SAGE.
