Adjusted Boxplot Outlier Detection (Medcouple)

The adjusted boxplot flags outliers with fences that are widened on the skewed side according to the medcouple, a robust measure of skewness, so skewed data are not over-flagged.

조정 상자그림은 강건한 왜도 지표인 medcouple에 따라 치우친 쪽 울타리를 넓혀, 치우친 자료에서 정상값을 이상치로 과하게 잡지 않도록 하는 이상치 탐지법입니다.

My income variable is right-skewed and the usual boxplot rule marks too many high values as outliers; what should I use?

소득 변수가 오른쪽으로 치우쳐서 일반 상자그림 기준으로는 높은 값이 너무 많이 이상치로 잡혀요. 무엇을 써야 하나요?

The adjusted boxplot keeps the quartiles and interquartile range of the usual rule but multiplies the fence lengths by exponential factors of the medcouple, extending the fence on the long tail and shortening it on the short tail. For symmetric data the medcouple is zero and the rule is the same as Tukey's boxplot.

When to use Adjusted Boxplot Outlier Detection (Medcouple)

• A single continuous variable is skewed and you need an outlier screen.
• Tukey's 1.5 × IQR rule flags many points in the long tail of a skewed distribution.
• You want a robust check alongside a Hampel (median and MAD) filter.

When to use something else

• Data are roughly normal and you want a formal test for one outlier; use Grubbs' test.
• Outliers must be judged jointly over several variables; use robust multivariate (MCD) outlier detection.

Assumptions and requirements

• Observations come from one unimodal distribution.
• Skewness is moderate (medcouple between about −0.6 and 0.6).
• Quartiles use linear interpolation, so results may differ slightly from hinge-based software.

What the analysis reports

• Medcouple, quartiles and interquartile range
• Lower and upper adjusted fences and the count of flagged values
• Comparison with the Tukey rule and the Hampel filter
• Table of flagged rows with value and side

How to report it

Using the adjusted boxplot rule (MC = [value]; fences [[value], [value]]), [value] of [N] observations were flagged as outliers, compared with [value] under the Tukey rule.

Related methods

• Grubbs' Outlier Test
• Generalized ESD Outlier Test
• Robust Multivariate Outlier Detection (MCD)

Run Adjusted Boxplot Outlier Detection (Medcouple) on Quorant