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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 Correlation ratio ： ウィキペディア英語版 Correlation ratio In statistics, the correlation ratio is a measure of the relationship between the statistical dispersion within individual categories and the dispersion across the whole population or sample. The measure is defined as the ''ratio'' of two standard deviations representing these types of variation. The context here is the same as that of the intraclass correlation coefficient, whose value is the square of the correlation ratio. ==Definition== Suppose each observation is ''yxi'' where ''x'' indicates the category that observation is in and ''i'' is the label of the particular observation. Let ''nx'' be the number of observations in category ''x'' and :$\backslash overline\_x=\backslash frac$ and $\backslash overline=\backslash frac,$ where $\backslash overline\_x$ is the mean of the category ''x'' and $\backslash overline$ is the mean of the whole population. The correlation ratio η (eta) is defined as to satisfy :$\backslash eta^2\; =\; \backslash frac)^2\}-\backslash overline)^2\}$ which can be written as :$\backslash eta^2\; =\; \backslash frac\}^2\}^2\},\; \backslash text^2\; =\; \backslash frac)^2\}\; \backslash text\; (y\_-\backslash overline)^2\},$ i.e. the weighted variance of the category means divided by the variance of all samples. It is worth noting that if the relationship between values of $x\; \backslash ;\backslash$ and values of $\backslash overline\_x$ is linear (which is certainly true when there are only two possibilities for ''x'') this will give the same result as the square of Pearson's correlation coefficient, otherwise the correlation ratio will be larger in magnitude. It can therefore be used for judging non-linear relationships. 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「Correlation ratio」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.