What is the acceptable range of skewness and kurtosis for normal distribution of data?
First of all, the definition is set as kurtosis=3 and skewness=0 to refer to the univariate normal distribution (uniform distribution). So this would lead to a normal distribution when the values are centered around 0. Note: kurtosis is often reported as EXCESS of kurtosis, which refers to the difference between the empirical kurtosis and the kurtosis of the normal distribution (i.e. 3), so the excess is 0 for a normal distribution.
Now about the acceptability: here we should think about what kind of acceptability do you have in mind (or asked in another way: for which reason are you interested in this statement?)—is it about deviations from normal distribution?
Typically, you find the following criterion: skewness [-0.5; 0.5]: “fairly symmetrical”, including fully symmetrical; [-1; – 0.5] or [0.5; 1]: “moderately skewed”; if your distribution shows a skewness of 1, we define this distribution as “highly skewed”.
Regarding kurtosis, here excess of kurtosis: if the excess lies in the range of [-1; 1] we are very close to the normal distribution.
But you see all these recommendations are very very crude and somehow arbitrary. Whether these are ACCEPTABLE for your research is a different story, but you can rawly orient to these values as some important landmark points.
All the best,
CCC
Skewness. A measure of the asymmetry of a distribution. The normal distribution is symmetric and has a skewness value of 0. A distribution with a significant positive skewness has a long right tail. A distribution with a significant negative skewness has a long left tail. As a guideline, a skewness value more than twice its standard error is taken to indicate a departure from symmetry.Standard Error of Skewness. The ratio of skewness to its standard error can be used as a test of normality (that is, you can reject normality if the ratio is less than -2 or greater than +2). A large positive value for skewness indicates a long right tail; an extreme negative value indicates a long left tail.Kurtosis. A measure of the extent to which observations cluster around a central point. For a normal distribution, the value of the kurtosis statistic is zero. Positive kurtosis indicates that, relative to a normal distribution, the observations are more clustered about the center of the distribution and have thinner tails until the extreme values of the distribution, at which point the tails of the leptokurtic distribution are thicker relative to a normal distribution. Negative kurtosis indicates that, relative to a normal distribution, the observations cluster less and have thicker tails until the extreme values of the distribution, at which point the tails of the platykurtic distribution are thinner relative to a normal distribution.Standard Error of Kurtosis. The ratio of kurtosis to its standard error can be used as a test of normality (that is, you can reject normality if the ratio is less than -2 or greater than +2). A large positive value for kurtosis indicates that the tails of the distribution are longer than those of a normal distribution; a negative value for kurtosis indicates shorter tails (becoming like those of a box-shaped uniform distribution).
https://www.ibm.com/support/knowledgecenter/en/SS3RA7_15.0.0/com.ibm.spss.modeler.help/dataaudit_displaystatistics.htm
K. V. MARDIA, Measures of multivariate skewness and kurtosis with applications, Biometrika, Volume 57, Issue 3, December 1970, Pages 519–530, https://doi.org/10.1093/biomet/57.3.519
there is no clear cut criteria for skewness and kurtosis. it depends on the nature of your data and research problem. generally people accept ± 1.96 for skewness.
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