Dear Mustafa,

I presume your sig. value was < 0.05, not 0.5.

I agree with Mahmaod that you should divide the statistic values for skewness and kurtosis by their standard error. Anything 2 is significant. There should be some correspondence between this and your sig value result. However, it is possible to have a non-normal distribution with non-significant skewness and kurtosis.

The decision of whether to treat your data as normally distributed is not as important as whether it is possible to run a parametric test. With a sample size of 500 many parametric tests are still reliable even for non-normal data - this is known as robust use. The particular conditions for robust use will depend upon the test you are using.

I remember that I asked Professor Jim Schwab few years ago similar question and his answer was: 

....

The rule of thumb I use is to compare the value for skewness to +/- 1.0. You do not divide by the standard error.

A different rule of thumb divides skewness by standard error of skewness and compares the result to 2 (approximately 1.96 for z at p=.05. If the result is greater than +/- 2.0, the variable has a skewness problem.

hope this helps 

Dear Mustafa,

I presume your sig. value was < 0.05, not 0.5.

I agree with Mahmaod that you should divide the statistic values for skewness and kurtosis by their standard error. Anything 2 is significant. There should be some correspondence between this and your sig value result. However, it is possible to have a non-normal distribution with non-significant skewness and kurtosis.

The decision of whether to treat your data as normally distributed is not as important as whether it is possible to run a parametric test. With a sample size of 500 many parametric tests are still reliable even for non-normal data - this is known as robust use. The particular conditions for robust use will depend upon the test you are using.

Dear Mustafa,

I have seen +/- 2.0 (Schutz ve Gessaroli, 1993, p. 918). Its pretty old source yet still valid.

Goodluck mate

So the tests for normality were significant (

Looking at just the skewness or the kurtosis and comparing them with zero or 3 which are the normal distribution respective values sounds naive. The test I often use is the Jarque-Bera test of normality of distribution which is based not just on skewness and kurtosis. It is based on a composite function of skewness, kurtosis, degree of freedom and number of regressors. That sounds more realistic than just considering a confidence interval of skewness or kurtosis.

we described a new methodology in order to measure skewness. j.ponte.2017.2.34

I agree with Professor Ette Etuk answer.He is good in the filed.

A large sample can yield a statistically significant non-normality even if the departure from normality is, substantively, trivial. If your sample is very much larger than 500, you may well be in that situation. Besides just looking at the skewness and kurtosis values, examine a histogram of the data. If it looks pretty "normal" (mounded in the middle, roughly symmetrical on each side, reasonable outliers) then you are probably safe in ignoring the non-normality. As others in this thread have noted, many parametric statistical methods are quite robust to the normality assumption when the sample size is large.

The 'test of normality' such as Kolmogorov-Simirnov and Shapiro-Wilk are often found to be questionable. Thus many researchers as you have mentioned often rely on the value of Kurtosis and Skewness. I am adding a file. Hope it helps.

Some says for skewness (−1,1) and (−2,2) for kurtosis is an acceptable range for being normally distributed. Some says (−1.96,1.96) for skewness is an acceptable range.

for skewness -2 to +2 and for kurtosis -9 to +9

Please see the reference below for skewness and kurtosis recommended values of less than |2.0| and |9.0| respectively.

Schmider, E., Ziegler, M., Danay, E., Beyer, L., & Bühner, M. (2010). Is it really robust? Reinvestigating the robustness of ANOVA against violations of the normal distribution assumption. Methodology: European Journal of Research Methods for the Behavioral and Social Sciences, 147-151.

If skewness is less than -1 or greater than 1, the distribution is highly skewed. If skewness is between -1 and -0.5 or between 0.5 and 1, the distribution is moderately skewed. If skewness is between -0.5 and 0.5, the distribution is approximately symmetric.