Grubbs' Outlier Test

Grubbs' test is a test of whether the single most extreme value in an approximately normal sample is an outlier, based on its distance from the mean in standard deviation units.

Grubbs 검정은 정규분포에 가까운 표본에서 평균으로부터 가장 멀리 떨어진 값 하나가 이상치인지를 표준편차 단위 거리로 검정하는 방법이다.

How do I formally test whether the most extreme value in my data is an outlier?

자료에서 가장 극단적인 값 하나가 이상치인지 통계적으로 검정하려면 어떻게 해야 하나요?

Grubbs' test computes G, the largest absolute deviation from the sample mean divided by the sample SD, and compares it with a critical value derived from the t distribution. It tests only one suspected value at a time and assumes the remaining data are normal.

When to use Grubbs' Outlier Test

• You suspect exactly one outlier in a univariate sample.
• The rest of the data are approximately normal.
• The sample has at least about seven observations.

When to use something else

• Several outliers may be present; use the generalized ESD test instead.
• The data are clearly non-normal; use an IQR or median absolute deviation rule instead.

Assumptions and requirements

• Apart from the suspect value, the data come from a normal distribution.
• Observations are independent.

What the analysis reports

• G statistic
• Critical G at the chosen α
• P-value
• Suspect value and its position

How to report it

A two-sided Grubbs' test [identified/did not identify] the value [value] as an outlier, G = [value], critical G = [value], p = [value].

Related methods

• Generalized ESD Outlier Test
• Robust Multivariate Outlier Detection (MCD)
• Robust Location and Scale Estimates

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