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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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https://doi.org/10.1007/BFb0030982her by Kageyama, 1976a; see also John, 1987, Section 3.4). Whereas in an ordinary block design (as considered in Section 3.2) the stratification of the experimental units leads to three strata, of units within blocks, of blocks within the total experimental area, and of the total area, in the extend
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General Block Designs and Their Statistical Properties,32 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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Introduction,ing the construction of the experiment is available. More precisely, the method is to be derived from a model reflecting unambiguously the structure of 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 exper
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General Block Designs and Their Statistical Properties, be random-ized before they enter the experiment. Suppose that to apply a general block design, in the sense of Section 2.2, randomization is performed as described by Nelder (1954), i.e., by randomly permuting blocks within a total area of them and by randomly permuting units within the blocks. The
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Balance and Efficiency:Classification of Notions,roportion-ality of them (Section 2.4.2). These notions have been formulated and discussed in terms of constructional features of the design, leaving their statistical impli-cations to the time when a model for the variables observed in the experiment is adopted and its properties are fully establish
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