If skewness is between +1/-1 and kurtosis is between +3/-3 but Kolmogorov-Smirnov test has significance <0.01, does the data is normally distributed?

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Cristian Ramos-Vera

Also depending on the sample size can perform the Mardia coefficient.

Ilhan Yandi

No, according to Kolmogorov-Smirnov result (p

Sinan Mavruk

Normality tests tend to give significant violation from the normal distribution if your sample size is high. Your sample size is not bad. Try visually investigate your data with a qq plot and if there is not an apparent violation from the qq line you can make a normal assumption and go on with your hypothesis tests. PS. Other assumptions should still be tested !!