Skewness

Definition

Skewness is a measure of the asymmetry of a probability distribution. A distribution is right-skewed (positive skew) when the tail on the right side is longer or fatter than the left, indicating a concentration of smaller values with a few extreme large ones. Left-skewed (negative) distributions have the opposite pattern. Symmetric distributions, such as the normal distribution, have skewness near zero.

Why It Matters

Skewness determines whether the mean or the median is the more appropriate measure of central tendency. It also influences the choice of statistical tests: parametric tests assume approximate normality, which is violated by highly skewed data. Recognising skewness prompts researchers to apply transformations (such as log or square-root) or to switch to non-parametric methods that do not assume symmetry.

Example

Household income data are typically right-skewed: most households earn moderate incomes, while a small percentage earn extremely high salaries. In the UK, the mean household income might be £45,000, but the median is only £35,000. The positive skewness tells analysts that the mean is inflated by high earners, and that the median better represents the typical household. A researcher might therefore log-transform income before running a regression.

Related Terms

• Normal Distribution
• Mean
• Median
• Kurtosis
• Outlier

Software Notes

• SPSS: Analyze > Descriptive Statistics > Frequencies or Descriptives. Check "Skewness" under Statistics. SPSS also reports the standard error of skewness, allowing a rough z-test (skewness / SE > 2 suggests significant skew).
• R: moments::skewness(x) or e1071::skewness(x). psych::describe(x) reports skewness alongside other descriptives. hist(x) with a density overlay visualises skew.
• Stata: summarize varname, detail reports skewness in the "Skewness" row. tabstat varname, statistics(skewness) for a focused table.