Adjusted Boxplot for Skewed Distributions
Also known as: adjusted box plot, medcouple boxplot, skewness-adjusted boxplot, Düzeltilmiş Kutu Grafiği (Adjusted Boxplot)
The Adjusted Boxplot is a robust descriptive tool introduced by Hubert and Vandervieren (2008) that corrects the classical IQR-based boxplot for skewness using the medcouple statistic, reducing the false labelling of outliers in asymmetric data.
Read the full method
Sign in with a free account to read this section.
Method map
The neighbourhood of related methods — select a node to explore.
When to use it
Use the adjusted boxplot when you are exploring or describing a single continuous variable whose distribution may be skewed and you want outlier detection that does not penalise the long tail. It assumes continuous data and tolerates, indeed expects, departures from symmetry; normality is not required. A reasonable sample size of at least about 20 observations is recommended so the medcouple is stable. It is less useful for tiny samples or when the contamination is so heavy that even adjusted fences cannot separate genuine outliers from the bulk of the data.
Strengths & limitations
- Corrects the classical boxplot for skewness, sharply reducing false outlier flags on asymmetric distributions.
- Built on the medcouple, a robust measure of skewness with a high breakdown point, so a few extreme values do not distort the fences.
- Reduces to the familiar 1.5·IQR boxplot when the data are symmetric, so it generalises rather than replaces the classical tool.
- On very small samples (n < 10) the medcouple statistic is unreliable and a standard boxplot is preferable.
- When the outlier ratio is very high (above about 25%), even the adjusted fences can be overwhelmed and fail to isolate the contamination.
- It is a univariate descriptive and detection tool, not an inferential model; it quantifies neither effect sizes nor uncertainty.
Frequently asked
How does the adjusted boxplot differ from a classical boxplot?
A classical boxplot places its fences symmetrically at 1.5·IQR from the quartiles, which over-flags points on the long tail of a skewed distribution. The adjusted boxplot multiplies those fences by an exponential factor based on the medcouple, stretching the long-tail side and shrinking the short-tail side so the fences match the data's shape.
What is the medcouple?
The medcouple (MC) is a robust measure of skewness that ranges from -1 to 1. It is computed from a kernel over pairs of observations straddling the median, is zero for symmetric data, positive for right skew and negative for left skew, and has a high breakdown point so a few extreme values do not corrupt it.
What sample size do I need?
At least about 20 observations are recommended for the medcouple to be stable. Below roughly 10 observations the medcouple becomes unreliable and a standard boxplot is the better choice.
What if my data are very heavily contaminated?
When the outlier ratio rises above about 25%, even the adjusted fences can be swamped, and the method may no longer separate genuine outliers from the bulk of the data. In that case a more deliberately robust scale estimate, such as the median absolute deviation, is a sounder basis for screening.
Sources
- Hubert, M. & Vandervieren, E. (2008). An Adjusted Boxplot for Skewed Distributions. Computational Statistics & Data Analysis, 52(12), 5186-5201. DOI: 10.1016/j.csda.2007.11.008 ↗
How to cite this page
ScholarGate. (2026, June 1). Adjusted Boxplot for Skewed Distributions. ScholarGate. https://scholargate.app/en/statistics/adjusted-boxplot
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Bootstrap InferenceStatistics↔ compare
- JackknifeStatistics↔ compare
- MAD EstimationStatistics↔ compare
- Robust Time Series AnalysisStatistics↔ compare
- Sn and Qn Scale EstimatorsStatistics↔ compare