一般情况下随机区组设计的置换检验的大样本理论

一般情况下随机区组设计的置换检验的大样本理论 LARGE SAMPLE THEORY OF PERMUTATION TESTS IN THE GENERAL CASE OF RANDOMIZED BLOCK DESIGN 陈希孺 Chen Xiru 1 first-author 中国科技大学 中国科技大学 < 正 > §1.引言设有c个处理A 1 ,…,A c ,要在N个区组中进行比较,每个区组包含c个试验单元,恰够把每个处理各做一次。所谓"随机区组"。设计,就是在每个区组内,那一个处理分配给那一个试验单元按纯随机的方式决定,且在各区组内所施行的随机化手续是彼此独立的。在传统的方差分析中,用以描述这种设计的数学模型是 Suppose that there are c treatments to be compared in N blocks each containing exactly c experimental units. Denote the treatment effects by a 1 , …, a c and the unit effects in the j-th block by b 1j , …, b cj , and the random experimental error of the observation X ij of the i-th treatment in the j-th block by e ij , then the randomized block design can be expressed by X ij =a i +η ij +e ij , where (η ij , …, η cj ) is a random vector such that P{(η 1j , …, η cj )=（bi 1 j, …, bi c j）}=1/（c!） for each permutaton （i 1 , …, i c ） of （1, …, c）. It is shown in this paper that, under this general formulation, the permutation F-test has the same asymptotic power as the usual F-test. 1983-04-01 2021-04-01 4