Skewness and Kurtosis

Additional measures are the skewness and kurtosis used to compare our data set with one normally distributed. 

• 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 centre point. Skewness is demonstrated on a bell curve when data points are not distributed symmetrically to the left and right sides of the median on a bell curve. There are three types of skewness: 

• • Zero skew (which means that the data are normally distributed). 
  • Right skew (also called positive skew). A right-skewed distribution is longer on the right side of its peak than on its left. 
  • Left skew (also called negative skew). A left-skewed distribution is longer on the left side of its peak than on its right. 

• Kurtosis is a measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution. A standard normal distribution has kurtosis of 3 and is recognized as mesokurtic. Data sets that deviate from the normal distribution can be leptokurtic or platykurtic:  

• • Leptokurtic distributions are statistical distributions with kurtosis greater than three. It can be described as having a wider or flatter shape with fatter tails resulting in a greater chance of extreme positive or negative events. 

• • Platykurtic distributions are statistical distributions in which the excess kurtosis value is negative. For this reason, a platykurtic distribution will have thinner tails than a normal distribution will, resulting in fewer extreme positive or negative events. 

You can learn more about kurtosis in this video: 

You can learn more about skewness in this video: 

References 

Lazar, J. , Feng, J. H., Hochheiser, H.  (2017), Research methods in human-computer interaction: Morgan Kaufmann, 2017. 

Rosenthal, R., Rosnow, R., 2008. Essentials of Behavioral Research: Methods and Data Analysis, third ed. McGraw Hill, Boston, MA.