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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Grubbs' test for outliers ： ウィキペディア英語版 Grubbs' test for outliers Grubbs' test (named after Frank E. Grubbs, who published the test in 1950), also known as the maximum normed residual test or extreme studentized deviate test, is a statistical test used to detect outliers in a univariate data set assumed to come from a normally distributed population. ==Definition== Grubbs' test is based on the assumption of normality. That is, one should first verify that the data can be reasonably approximated by a normal distribution before applying the Grubbs' test.〔Quoted from the ''Engineering and Statistics Handbook'', paragraph 1.3.5.17, http://www.itl.nist.gov/div898/handbook/eda/section3/eda35h.htm〕 Grubbs' test detects one outlier at a time. This outlier is expunged from the dataset and the test is iterated until no outliers are detected. However, multiple iterations change the probabilities of detection, and the test should not be used for sample sizes of six or fewer since it frequently tags most of the points as outliers. Grubbs' test is defined for the hypothesis: :H0: There are no outliers in the data set :Ha: There is at least one outlier in the data set The Grubbs' test statistic is defined as: :$$ G = \frac\right\vert} with $\backslash overline$ and $s$ denoting the sample mean and standard deviation, respectively. The Grubbs test statistic is the largest absolute deviation from the sample mean in units of the sample standard deviation. This is the two-sided version of the test. The Grubbs test can also be defined as a one-sided test. To test whether the minimum value is an outlier, the test statistic is :$$ G = \frac with ''Y''min denoting the minimum value. To test whether the maximum value is an outlier, the test statistic is :$$ G = \frac with ''Y''max denoting the maximum value. For the two-sided test, the hypothesis of no outliers is rejected at significance level α if :$$ G > \frac^2}} with ''t''α/(2''N''),''N''−2 denoting the upper critical value of the t-distribution with ''N'' − 2 degrees of freedom and a significance level of α/(2''N''). For the one-sided tests, replace α/(2''N'') with α/''N''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Grubbs' test for outliers」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.