Introduction
This topic describes the shape of a numerical distribution beyond its centre and spread. Skewness describes how asymmetric the distribution is, and kurtosis describes how heavy its tails are compared with the normal distribution. Both are needed to judge whether summary statistics and standard tests are appropriate for a given set of medical data.
What skewness measures
Skewness is the asymmetry of a distribution around its mean. In a symmetric distribution, such as the normal distribution, the two halves are mirror images and the skewness is zero. The usual sample coefficient, the moment coefficient of skewness, is based on the third central moment:
Because the deviations are cubed, they keep their sign, and large deviations on one side dominate. A positive value means a longer right tail (right-skewed), and a negative value means a longer left tail (left-skewed). Statistical software often reports an adjusted version for small samples, so the numbers may differ slightly from the formula.