Grubbs' test for outliers

The Grubbs outlier test is a statistical test that is used to detect outliers in a given sample to eliminate and by iteration to improve the remaining sample. The outlier test Nalimov is a variant of the outlier test according to Grubbs.

Requirements

Prerequisite for the application of the Grubbs test the hypothesis that the data are approximately normally distributed. This can be derived from theoretical considerations or in general by testing for normal distribution for the source of the data or the sample to be checked specifically. The test should be carried out without the putative outliers, as these can distort the test statistic otherwise.

Test statistic

Then from the sample, the test statistic

Calculated in the

The mean and the variance of the sample, respectively. Under the null hypothesis that there are no outliers exist, has a distribution which can be represented as a function of t-distribution. Consequently, the test is rejected at the significance level, if with

Applies. It generally refers to the critical value of a t-distribution with degrees of freedom to the level.

If the test actually discovered an outlier, the date in question is removed from the sample and performed a new Grubbs test with data in the remaining sample. This should be done so long before using the test no more outliers can be detected.

Variants

• A variant of the Grubbs' test is to want to discover only outlier upwards or downwards. This is achieved in that, instead of adjusting or only observed and the critical value of the test statistic on.

• The outlier test Nalimov modifies the test statistic G with a time dependent on sample size correction factor:

Swell

• Frank E. Grubbs: Sample Criteria for Testing Outlying Observations. In: The Annals of Mathematical Statistics. 21, No. 1, 1950, pp. 27-58, doi: 10.1214/aoms/1177729885.
• Frank E. Grubbs: Procedures for Detecting Outlying Observations in Samples. In: Technometrics. 11, No. 1, January 1, 1969, pp. 1-21, doi: 10.2307/1266761.
• Chapter 1.3.5.17. Grubbs ' test for outliers. In: Carroll Croarkin, Paul Tobias (ed.) NIST / SEMATECH e - Handbook of Statistical Methods.
• DIN 53 804 Part 1, Statistical Analysis - Measurable (continuous ) features. Section 8.2 outlier test according to Grubbs, September 1981
• DIN ISO 5725 Part 2, Accuracy (trueness and precision) of measurement methods and results - A basic method for the determination of repeatability and reproducibility of a standard measurement method. Section 14.4 Grubbs ' test, draft February 1991

Online calculator

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• Parametric test