The main estimation and hypothesis testing results related to the Gauss- Markov model, in its general form, are recalled and the application of these results to the analysis of experiments in block designs is considered. Special attention is given to the randomization-derived model for a general block design, and for a proper block design in particular. The question whether the randomization-derived model can be considered as a particular general Gauss-Markov model is discussed. It is indicated...
Summary The main estimation and hypothesis testing results are presented for experiments conducted in proper block designs. It is shown that, under appropriate randomization, these experiments have the convenient orthogonal block structure. Because of this, the analysis of experimental data can be performed in a comparatively simple way. Certain simplifying procedures are introduced. The main advantage of the presented methodology concerns the analysis of variance and related hypothesis testing...
Partially efficiency balanced (PEB) designs with m efficiency classes have been defined by Puri and Nigam [15] as block designs which have simple analysis and, if properly used, allow the important contrasts to be estimated with desired efficiency. Such designs can be made available in varying replications and/or unequal block sizes. However, any block design is a PEB design with m efficiency classes for some m < v, where v is the number of treatments in the design. So the term "PEB" itself is...
The authors examine the estimation of basic contrasts of treatment parameters in incomplete multiresponse block designs (IMBDs). The basic definitions and the preliminary discussion of IMBDs are the same as those of J. N. Srivastava [Ann. Math. Statist. 39 (1968), 1825–1843; MR0233468]. For the estimation of treatment contrasts in IMBDs, the authors make use of the theory of basic contrasts given by S. C. Pearce, the first author and T. F. de C. Marshall [Biometrika 61 (1974), 449–460; MR0386176]....
The authors discuss the interconnections between the concepts of orthogonality, efficiency, and balance of block designs. No new theorems are obtained. Illustrative examples are presented. MR0707816
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