Generalized ESD Outlier Test

The generalized extreme Studentized deviate (ESD) test is a sequential procedure that detects up to a prespecified number of outliers in an approximately normal sample.

일반화 ESD 검정은 정규분포에 가까운 표본에서 미리 정한 최대 개수까지 가장 먼 값을 하나씩 떼어 가며 여러 이상치를 순차적으로 찾아내는 검정이다.

How do I test for several outliers at once without one outlier hiding another?

이상치가 여러 개일 때 하나가 다른 하나를 가리지 않도록 한꺼번에 검정하는 방법이 있나요?

The generalized ESD test removes the most extreme value step by step up to r times, computing a test statistic R_i and a critical value λ_i at each step. The number of outliers is the largest i for which R_i exceeds λ_i, which protects against masking when outliers are similar in size.

When to use Generalized ESD Outlier Test

• Several outliers may be present in a univariate sample.
• An upper limit on the number of outliers can be stated.
• The bulk of the data is approximately normal.

When to use something else

• At most one outlier is expected; use Grubbs' test instead.
• The data are strongly skewed; transform them first or use a robust rule based on the median absolute deviation.

Assumptions and requirements

• Without outliers the data are approximately normal.
• Observations are independent.
• The maximum number of outliers is specified in advance (default: 10% of n, at most 10).

What the analysis reports

• R_i and λ_i for each step
• Number of detected outliers
• Values flagged as outliers

How to report it

A generalized ESD test with up to [r] suspected outliers (α = [value]) identified [k] outliers ([values]) in N = [value] observations.

Related methods

• Grubbs' Outlier Test
• Robust Multivariate Outlier Detection (MCD)
• Isolation Forest Anomaly Detection

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