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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 intraclass correlation ： ウィキペディア英語版 intraclass correlation In statistics, the intraclass correlation (or the ''intraclass correlation coefficient'', abbreviated ICC) is a descriptive statistic that can be used when quantitative measurements are made on units that are organized into groups. It describes how strongly units in the same group resemble each other. While it is viewed as a type of correlation, unlike most other correlation measures it operates on data structured as groups, rather than data structured as paired observations. The ''intraclass correlation'' is commonly used to quantify the degree to which individuals with a fixed degree of relatedness (e.g. full siblings) resemble each other in terms of a quantitative trait (see heritability). Another prominent application is the assessment of consistency or reproducibility of quantitative measurements made by different observers measuring the same quantity. == Early ICC definition: unbiased but complex formula == The earliest work on intraclass correlations focused on the case of paired measurements, and the first intraclass correlation (ICC) statistics to be proposed were modifications of the interclass correlation (Pearson correlation). Consider a data set consisting of ''N'' paired data values (''x''''n'',1, ''x''''n'',2), for ''n'' = 1, ..., ''N''. The intraclass correlation ''r'' originally proposed by Ronald Fisher is : $r\; =\; \backslash frac\; \backslash sum\_^\; (x\_\; -\; \backslash bar)\; (\; x\_\; -\; \backslash bar)$, where : $\backslash bar\; =\; \backslash frac\; \backslash sum\_^\; (x\_\; +\; x\_)$, : $s^2\; =\; \backslash frac\; \backslash left\backslash \; (\; x\_\; -\; \backslash bar)^2\; +\; \backslash sum\_^\; (\; x\_\; -\; \backslash bar)^2\; \backslash right\backslash \}$. Later versions of this statistic used the degrees of freedom 2''N'' −1 in the denominator for calculating ''s''2 and ''N'' −1 in the denominator for calculating ''r'', so that ''s''2 becomes unbiased, and ''r'' becomes unbiased if ''s'' is known. The key difference between this ICC and the interclass (Pearson) correlation is that the data are pooled to estimate the mean and variance. The reason for this is that in the setting where an intraclass correlation is desired, the pairs are considered to be unordered. For example, if we are studying the resemblance of twins, there is usually no meaningful way to order the values for the two individuals within a twin pair. Like the interclass correlation, the intraclass correlation for paired data will be confined to the interval (+1 ). The intraclass correlation is also defined for data sets with groups having more than 2 values. For groups consisting of 3 values, it is defined as〔 : $r\; =\; \backslash frac\; \backslash sum\_^\; \backslash left\backslash )(\; x\_\; -\; \backslash bar)\; +\; (x\_\; -\; \backslash bar)(\; x\_\; -\; \backslash bar)+(\; x\_\; -\; \backslash bar)(\; x\_\; -\; \backslash bar)\; \backslash right\backslash \}$, where : $\backslash bar\; =\; \backslash frac\; \backslash sum\_^\; (x\_\; +\; x\_\; +\; x\_)$, : $s^2\; =\; \backslash frac\; \backslash left\backslash \; (\; x\_\; -\; \backslash bar)^2\; +\; \backslash sum\_^\; (\; x\_\; -\; \backslash bar)^2\; +\; \backslash sum\_^\; (\; x\_\; -\; \backslash bar)^2\backslash right\backslash \}$. As the number of values per groups grows, the number of cross-product terms in this expression grows rapidly. The equivalent form :$r\; =\; \backslash frac\backslash cdot\backslash frac^N(\backslash bar\_n-\backslash bar)^2\}\; -\; \backslash frac,$ where ''K'' is the number of data values per group, and $\backslash bar\_n$ is the sample mean of the ''n''th group, is simpler to calculate.〔 This form is usually attributed to Harris. The left term is non-negative, consequently the intraclass correlation must satisfy : $r\; \backslash geq\; -1\; /(K-1)$. For large ''K'', this ICC is nearly equal to :$$ \frac^N(\bar_n-\bar)^2}, which can be interpreted as the fraction of the total variance that is due to variation between groups. Ronald Fisher devotes an entire chapter to Intraclass correlation in his classic book ''Statistical Methods for Research Workers''.〔 For data from a population that is completely noise, Fisher's formula produces ICC values that are distributed about 0, i.e. sometimes being negative. This is because Fisher designed the formula to be unbiased, and therefore its estimates are sometimes overestimates and sometimes underestimates. For small or 0 underlying values in the population, the ICC calculated from a sample may be negative. 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「intraclass correlation」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.