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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 Analysis of covariance ： ウィキペディア英語版 Analysis of covariance Analysis of covariance (ANCOVA) is a general linear model which blends ANOVA and regression. ANCOVA evaluates whether population means of a dependent variable (DV) are equal across levels of a categorical independent variable (IV) often called a treatment, while statistically controlling for the effects of other continuous variables that are not of primary interest, known as covariates (CV) or nuisance variables. Mathematically, ANCOVA decomposes the variance in the DV into variance explained by the CV(s), variance explained by the categorical IV, and residual variance. Intuitively, ANCOVA can be thought of as 'adjusting' the DV by the group means of the CV(s).〔Keppel, G. (1991). ''Design and analysis: A researcher's handbook'' (3rd ed.). Englewood Cliffs: Prentice-Hall, Inc.〕 The ANCOVA procedure is described as follows, assuming that a linear relationship between the response (DV) and covariate (CV) exists: $y\_\; =\; \backslash mu\; +\; \backslash tau\_i\; +\; \backslash Beta(x\_\; -\; \backslash overline)\; +\; \backslash epsilon\_$ where $y\_$ is the jth observation under the ith categorical group, $\backslash mu$ is the grand mean, $\backslash tau\_i$ is the effect of the ith level of the IV, $x\_$ is the jth observation of the covariate under the ith group, $\backslash overline$ is the ith group mean, and $\backslash epsilon\_$ is the associated unobserved error term. Under this specification, we assume that the categorical treatment effects sum to zero $\backslash left(\backslash sum\_i^a\; \backslash tau\_i\; =\; 0\backslash right).$ The standard assumptions of the linear regression model are also assumed to hold, as discussed below.〔Montgomery, Douglas C. "Design and analysis of experiments" (8th Ed.). John Wiley & Sons, 2012.〕 ==Uses of ANCOVA== 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「Analysis of covariance」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.