Statistical theory of the analysis of experimental designs

Abstract

(Abstracts of papers presented at the Annual Meeting of the Statistical Science Association of Canada; May 29, 30, 31, 1975. / R$eAsum$eAs des articles pr$eAsent$eAs au congres annuel; 29, 30, 31 mai 1975; University of Alberta, Edmonton, Alberta.)

Cumulants and partition lattices VI. variances and covariances of mean squares

“…The following calculations are easy to perform : [s|i2(12,12) In this form this is just the result obtained by Pitman (1937) and Welch (1937); see also Kempthorne (1952), Wilk (1955) and Ogawa (1961Ogawa ( , 1974.…”

“…The first work in this area was by Welch (1937) who considered the randomized complete block design (RCBD) and Latin square designs (LSDs), and Pitman (1935), who independently derived not just the first two but the first four moments of the permutation distribution of the treatment mean square in a RCBD. In a number of papers Ogawa has extended this work to partially balanced incomplete block designs, see Ogawa (1974) and references therein; indeed he goes further in computing an approximate permutation beta-distribution for the non-centrality parameter of the usual F-test for significance of treatments, integrating out this terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S1446788700032158 [16] Cumulants and partitition lattices 377 parameter, and obtaining the usual central F-test.…”

“…We draw particular attention to the generalized cumulants which vanish when additivity models are assumed. The second set of results consist of re-derivations of the randomization variances given by P i t m a n (1937) and Welch (1937), see also Ogawa (1974), for the treatment mean square in randomized block and Latin square designs. Not only are our derivations rather more compact than those in the references cited, using the machinery developed in this series of papers, but it is also of T. P. Speed and H. L. SUcock [3] interest to see the same non-additivity and inhomogeneity measures appearing in this context as well.…”

Randomization analysis of covariance and change-over designs

“…by Eden and Yates (1933) and others, that the significance level that is obtained by this process is "close to" the significance level that is obtained by using the upper tail area of the associated normal distribution theory. Theoretical work on this was done by Pitman (1937), Welch (1937), Ogawa (1974) and Arnold (1964).…”

“…In Chapters 3 and 4 of this thesis we will examine the behavior under randomization of the usual Gauss-Markov normal theory statistics in the presence of concomitant 26 variation for these two designs. Pitman (1937) and Welch (1937) Ogawa (1974) and Arnold (1964). Pitman (1937) investigated the problem of testing the null hypothesis that the treatments are all equal in the randomized block design for univariate situations.…”