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Titlebook: Block Designs: A Randomization Approach; Volume I: Analysis Tadeusz Caliński,Sanpei Kageyama Book 2000 Springer Science+Business Media New

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發(fā)表于 2025-3-21 20:04:54 | 只看該作者 |倒序瀏覽 |閱讀模式
期刊全稱Block Designs: A Randomization Approach
期刊簡稱Volume I: Analysis
影響因子2023Tadeusz Caliński,Sanpei Kageyama
視頻videohttp://file.papertrans.cn/190/189163/189163.mp4
學科分類Lecture Notes in Statistics
圖書封面Titlebook: Block Designs: A Randomization Approach; Volume I: Analysis Tadeusz Caliński,Sanpei Kageyama Book 2000 Springer Science+Business Media New
影響因子In most of the literature on block designs, when considering the analysis of experimental results, it is assumed that the expected value of the response of an experimental unit is the sum of three separate components, a general mean parameter, a parameter measuring the effect of the treatment applied and a parameter measuring the effect of the block in which the experimental unit is located. In addition, it is usually assumed that the responses are uncorrelated, with the same variance. Adding to this the assumption of normal distribution of the responses, one obtains the so-called "normal-theory model" on which the usual analysis of variance is based. Referring to it, Scheffe (1959, p. 105) writes that "there is nothing in the ‘normal-theory model‘ of the two-way layout . . . that reflects the increased accuracy possible by good blocking. " Moreover, according to him, such a model "is inappropriate to those randomized-blocks experiments where the ‘errors‘ are caused mainly by differences among the experimental units rather than measurement errors. " In view of this opinion, he has devoted one of the chapters of his book (Chapter 9) to randomization models, being convinced that "an
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Philippe G. Ciarlet,Patrick Rabierf the experimental material, the actual use of it in the experiment, and the design according to which treatments that are to be compared in the experiment are assigned to the units of the material (i.e., to experimental units or plots).
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https://doi.org/10.1007/BFb0030982heir statistical impli-cations to the time when a model for the variables observed in the experiment is adopted and its properties are fully established. Because this task has been accomplished in Chapter 3, it is now possible to consider the statistical meaning of the various notions of balance, those considered in Section 2.4 in particular.
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Introduction,f the experimental material, the actual use of it in the experiment, and the design according to which treatments that are to be compared in the experiment are assigned to the units of the material (i.e., to experimental units or plots).
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https://doi.org/10.1007/BFb005839532 and Section 8.4; Ogawa, 1961, 1963; Hinkelmann and Kempthorne, 1994, Section 9.2.6), the model of the variables observed on the n units actually used in the experiment can be written in matrix notation as in (1.3.19), i.e., as.where y is an n x 1 vector of observed variables, . is a v x 1 vector
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