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In statistics, Grubbs's test or the Grubbs test (named after Frank E. Grubbs, who published the test in 1950 [1]), also known as the maximum normalized residual test or extreme studentized deviate test, is a test used to detect outliers in a univariate data set assumed to come from a normally distributed population.
Frank Ephraim Grubbs (September 2, 1913 – January 19, 2000) was an American statistician. Grubbs's test for outliers, and the Mann-Grubbs method for calculating a binomial series lower confidence bound, are named after him. He worked at the Ballistic Research Laboratory while he was a Captain in the U.S. Army.
The modified Thompson Tau test [citation needed] is a method used to determine if an outlier exists in a data set. The strength of this method lies in the fact that it takes into account a data set's standard deviation, average and provides a statistically determined rejection zone; thus providing an objective method to determine if a data ...
Another method for eliminating spurious data is called Peirce's criterion. It was developed a few years before Chauvenet's criterion was published, and it is a more rigorous approach to the rational deletion of outlier data. [3] Other methods such as Grubbs's test for outliers are mentioned under the listing for Outlier. [citation needed]
However, at 95% confidence, Q = 0.455 < 0.466 = Q table 0.167 is not considered an outlier. McBane [1] notes: Dixon provided related tests intended to search for more than one outlier, but they are much less frequently used than the r 10 or Q version that is intended to eliminate a single outlier.
The methods must manage real-time data, diverse device types, and scale effectively. Garbe et al. [19] have introduced a multi-stage anomaly detection framework that improves upon traditional methods by incorporating spatial clustering, density-based clustering, and locality-sensitive hashing. This tailored approach is designed to better handle ...
The t distribution is often used as an alternative to the normal distribution as a model for data, which often has heavier tails than the normal distribution allows for; see e.g. Lange et al. [14] The classical approach was to identify outliers (e.g., using Grubbs's test) and exclude or downweight them in
The Grubbs's test for outliers may be used to detect samples deviating from the group. A method for quality control in higher-dimensional space is to use probability binning with bins fit to the whole data set pooled together. [23]