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In randomized statistical experiments, generalized randomized block designs (GRBDs) are used to study the interaction between blocks and treatments. For a GRBD, each treatment is replicated at least two times in each block; this replication allows the estimation and testing of an interaction term in the linear model (without making parametric assumptions about a normal distribution for the error).〔 * Wilk, page 79. * Lentner and Biship, page 223. * Addelman (1969) page 35. * Hinkelmann and Kempthorne, page 314, for example; c.f. page 312. 〕 ==GRBDs versus RCBDs: Replication and interaction== Like a randomized complete block design (RCBD), a GRBD is randomized. Within each block, treatments are randomly assigned to experimental units: this randomization is also independent between blocks. In a (classic) RCBD, however, there is no replication of treatments within blocks.〔 * Wilk, page 79. * Addelman (1969) page 35. * Hinkelmann and Kempthorne, page 314. * Lentner and Bishop, page 223. 〕 Without replication, the (classic) RCBD's linear model lacks a block-treatment interaction-term that may be estimated (using the randomization distribution rather than using a normal distribution for the error).〔 * Wilk, page 79. * Addelman (1969) page 35. * Lentner and Bishop, page 223. A more detailed treatment occurs in Chapter 9.7 in Hinkelmann and Kempthorne. (Hinkelmann and Kempthorne do discuss block-treatment interaction for more complicated blocking structures, like crossed-blocking factors in Chapter 9.6, and for forms of "non-additivity" that may be removed by transformations).〕 In the RCBD, the block-treatment interaction cannot be estimated using the randomization distribution; a fortiori there exists no "valid" (i.e. randomization-based) test for the block-treatment interaction in the analysis of variance (anova) of the RCBD.〔Wilk, Addelman, Hinkelmann and Kempthorne.〕 The distinction between RCBDs and GRBDs has been ignored by some authors, and the ignorance regarding the GRCBD has been criticized by statisticians like Oscar Kempthorne and Sidney Addelman.〔 * Complaints about the neglect of GRBDs in the literature and ignorance among practitioners are stated by Addelman (1969) page 35. 〕 The GRBD has the advantage that replication allows block-treatment interaction to be studied.〔 * Wilk, page 79. * Addelman (1969) page 35. * Lentner and Bishop, page 223. 〕 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 randomized block design」の詳細全文を読む スポンサード リンク
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