What Do Skewness and Kurtosis Represent?

Skewness is a measure of symmetry, or more precisely, the lack of symmetry. A distribution, or data set, is symmetric if it looks the same to the left and right of the center point. Kurtosis is a measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution.

1. What does kurtosis represent?
2. What does skewness represent?
3. What should skewness and kurtosis be?
4. How does skewness and kurtosis determine normality?

What does kurtosis represent?

Kurtosis is a measure of the tailedness of a distribution. Tailedness is how often outliers occur. Excess kurtosis is the tailedness of a distribution relative to a normal distribution. Distributions with medium kurtosis (medium tails) are mesokurtic. Distributions with low kurtosis (thin tails) are platykurtic.

What does skewness represent?

Skewness is a measure of the asymmetry of a distribution. A distribution is asymmetrical when its left and right side are not mirror images. You might want to calculate the skewness of a distribution to: Describe the distribution of a variable alongside other descriptive statistics.

What should skewness and kurtosis be?

The values for asymmetry and kurtosis between -2 and +2 are considered acceptable in order to prove normal univariate distribution (George & Mallery, 2010). Hair et al. (2010) and Bryne (2010) argued that data is considered to be normal if skewness is between ‐2 to +2 and kurtosis is between ‐7 to +7.

How does skewness and kurtosis determine normality?

To overcome this problem, a z-test is applied for normality test using skewness and kurtosis. A Z score could be obtained by dividing the skewness values or excess kurtosis value by their standard errors. For small sample size (n <50), z value ± 1.96 are sufficient to establish normality of the data.