翻訳と辞書 Words near each other ・ Generalized map ・ Generalized Maxwell model ・ Generalized mean ・ Generalized method of moments ・ Generalized minimal residual method ・ Generalized minimum-distance decoding ・ Generalized Multi-Protocol Label Switching ・ Generalized multidimensional scaling ・ Generalized multivariate log-gamma distribution ・ Generalized Music Plug-in Interface ・ Generalized Newtonian fluid ・ Generalized nondeterministic finite automaton ・ Generalized normal distribution ・ Generalized other ・ Generalized Ozaki cost function ・ Generalized p-value ・ Generalized Pareto distribution ・ Generalized permutation matrix ・ Generalized Petersen graph ・ Generalized phrase structure grammar ・ Generalized Pochhammer symbol ・ Generalized Poincaré conjecture ・ Generalized polygon ・ Generalized processor sharing ・ Generalized Procrustes analysis ・ Generalized pustular psoriasis ・ Generalized quadrangle ・ Generalized quantifier ・ Generalized randomized block design ・ Generalized relative entropy Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Generalized p-value ： ウィキペディア英語版 Generalized p-value In statistics, a generalized ''p''-value is an extended version of the classical ''p''-value, which except in a limited number of applications, provides only approximate solutions. Conventional statistical methods do not provide exact solutions to many statistical problems, such as those arising in mixed models and MANOVA, especially when the problem involves many nuisance parameters. As a result, practitioners often resort to approximate statistical methods or asymptotic statistical methods that are valid only with large samples. With small samples, such methods often have poor performance.〔 Use of approximate and asymptotic methods may lead to misleading conclusions or may fail to detect truly significant results from experiments. Tests based on generalized ''p''-values are exact statistical methods in that they are based on exact probability statements. While conventional statistical methods do not provide exact solutions to such problems as testing variance components or ANOVA under unequal variances, exact tests for such problems can be obtained based on generalized ''p''-values.〔Weerahandi (1995)〕〔Tsui & Weerahandi (1989)〕 In order to overcome the shortcomings of the classical ''p''-values, Tsui and Weerahandi〔 extended the classical definition so that one can obtain exact solutions for such problems as the Behrens–Fisher problem and testing variance components. This is accomplished by allowing test variables to depend on observable random vectors as well as their observed values, as in the Bayesian treatment of the problem, but without having to treat constant parameters as random variables. ==A simple case== To describe the idea of generalized ''p''-values in a simple example, consider a situation of sampling from a normal population with mean $\backslash mu$, and variance $\backslash sigma\; ^2$, suppose $\backslash overline$ and $S\; ^2$ are the sample mean and the sample variance. Inferences on all unknown parameters can be based on the distributional results :$Z\; =\; \backslash sqrt(\backslash overline\; -\; \backslash mu)/\; \backslash sigma\; \backslash sim\; N(0,1)$ and :$U\; =\; n\; S^2\; /\; \backslash sigma^2\; \backslash sim\; \backslash chi^2\; \_\; .$ Now suppose we need to test the coefficient of variation, $\backslash rho\; =\; \backslash mu\; /\backslash sigma$. While the problem is not trivial with conventional ''p''-values, the task can be easily accomplished based on the generalized test variable :$R\; =\; \backslash frac\; -\; \backslash frac$ = \frac \frac } ~-~ \frac is the observed value of $\backslash overline$ and $s$ is the observed value of $S$. Note that the distribution of $R$ and its observed value are both free of nuisance parameters. Therefore, a test of a hypothesis with a one-sided alternative such as can be based on the generalized ''p''-value $p\; =\; Pr(\; R\; \backslash ge\; \backslash rho\_0\; )$, a quantity that can be evaluated via Monte Carlo simulation or using the non-central t-distribution. 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「Generalized p-value」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.