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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 Brown–Forsythe test ： ウィキペディア英語版 Brown–Forsythe test In statistics, when a usual one-way ANOVA is performed, it is assumed that the group variances are statistically equal. If this assumption is not valid, then the resulting ''F''-test is invalid. The Brown–Forsythe test is a statistical test for the equality of group variances based on performing an ANOVA on a transformation of the response variable. The Brown–Forsythe test statistic is the F statistic resulting from an ordinary one-way analysis of variance on the absolute deviations from the median. ==Transformation== The transformed response variable is constructed to measure the spread in each group. Let : $$ z_=\left\vert y_ - \tilde_j \right\vert where $\backslash tilde\_j$ is the median of group ''j''. The Brown–Forsythe test statistic is the model ''F'' statistic from a one way ANOVA on ''zij'': : $F\; =\; \backslash frac\; \backslash frac\; n\_j\; (\backslash tilde\_-\backslash tilde\_)^2\}\; \backslash sum\_^\; (z\_-\backslash tilde\_)^2\}$ where ''p'' is the number of groups, ''nj'' is the number of observations in group ''j'', and ''N'' is the total number of observations. Also $\backslash tilde\_$ are the group means of the $z\_$ and $\backslash tilde\_$ is the overall mean of the $z\_$. If the variances are indeed heterogeneous, techniques that allow for this (such as the Welch one-way ANOVA) may be used instead of the usual ANOVA. Good (), noting that the deviations are linearly dependent, has modified the test so as to drop the redundant deviations. 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「Brown–Forsythe test」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.