翻訳と辞書 Words near each other ・ Cochranella punctulata ・ Cochranella ramirezi ・ Cochranella resplendens ・ Cochranella riveroi ・ Cochranella saxiscandens ・ Cochranella spiculata ・ Cochranella susatamai ・ Cochranella tangarana ・ Cochranella xanthocheridia ・ Cochrane–Africatown USA Bridge ・ Cochrane–Orcutt estimation ・ Cochranites ・ Cochrans Falls ・ Cochranton, Pennsylvania ・ Cochranville, Pennsylvania ・ Cochran–Armitage test for trend ・ Cochran–Mantel–Haenszel statistics ・ Cochu's blue tetra ・ Cochuah ・ Cochylidia ・ Cochylidia altivaga ・ Cochylidia contumescens ・ Cochylidia heydeniana ・ Cochylidia implicitana ・ Cochylidia liui ・ Cochylidia moguntiana ・ Cochylidia multispinalis ・ Cochylidia oblonga ・ Cochylidia richteriana ・ Cochylidia rupicola 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 Cochran–Armitage test for trend ： ウィキペディア英語版 Cochran–Armitage test for trend The Cochran–Armitage test for trend,〔 〕 named for William Cochran and Peter Armitage, is used in categorical data analysis when the aim is to assess for the presence of an association between a variable with two categories and a variable with ''k'' categories. It modifies the Pearson chi-squared test to incorporate a suspected ordering in the effects of the ''k'' categories of the second variable. For example, doses of a treatment can be ordered as 'low', 'medium', and 'high', and we may suspect that the treatment benefit cannot become smaller as the dose increases. The trend test is often used as a genotype-based test for case-control genetic association studies. ==Introduction== The trend test is applied when the data take the form of a 2 × ''k'' contingency table. For example, if ''k'' = 3 we have This table can be completed with the marginal totals of the two variables where ''R''1 = ''N''11 + ''N''12 + ''N''13, and ''C''1 = ''N''11 + ''N''21, etc. The trend test statistic is :$T\; \backslash equiv\; \backslash sum\_^k\; t\_i\; (N\_\; R\_2\; -\; N\_\; R\_1),$ where the ''t''''i'' are weights, and the difference ''N''1''i''''R''2 −''N''2''i''''R''1 can be seen as the difference between ''N''1''i'' and ''N''2''i'' after reweighting the rows to have the same total. The hypothesis of no association (the null hypothesis) can be expressed as: :$\backslash Pr(A=1|\; B=1)\; =\; \backslash cdots\; =\; \backslash Pr(A=1|\; B=k).$ Assuming this holds, then, using iterated expectation, :$\backslash operatorname(T)\; =\; \backslash operatorname\; \backslash left(\; \backslash operatorname(T|R\_1,R\_2)\; \backslash right)\; =\; \backslash operatorname\; (0)\; =\; 0.$ The variance can be computed by decomposition, yielding :$$ (T) = \frac \left(\sum_^kt_i^2C_i(N-C_i) - 2\sum_^\sum_^kt_it_jC_iC_j\right), and as a large sample approximation, :$\backslash frac\}\; \backslash sim\; \backslash mathrm(0,1).$ The weights ''t''''i'' can be chosen such that the trend test becomes locally most powerful for detecting particular types of associations. For example, if ''k'' = 3 and we suspect that ''B'' = 1 and ''B'' = 2 have similar frequencies (within each row), but that ''B'' = 3 has a different frequency, then the weights ''t'' = (1,1,0) should be used. If we suspect a linear trend in the frequencies, then the weights ''t'' = (0,1,2) should be used. These weights are also often used when the frequencies are suspected to change monotonically with ''B'', even if the trend is not necessarily linear. 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「Cochran–Armitage test for trend」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.