Biometrical Letters Vol. 54(2), 2017, pp. 91-122
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ON A NEW APPROACH TO THE ANALYSIS OF VARIANCE FOR EXPERIMENTS WITH ORTHOGONAL BLOCK STRUCTURE. I. EXPERIMENTS IN PROPER BLOCK DESIGNS Tadeusz Calinski, Idzi Siatkowski Department of Mathematical and Statistical Methods, Poznan University of Life Sciences, Wojska Polskiego 28, 60-637 Poznan, Poland, e-mail: calinski@up.poznan.pl, idzi.siatkowski@up.poznan.pl |
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 procedures. Under the adopted approach one can perform them directly, not by combining results from intra-block and inter-block analyses. Application of the theory is illustrated by three examples of real experiments in proper block designs. This is the first of a projected series of papers concerning the analysis of experiments with orthogonal block structure.
analysis of variance, estimation, hypothesis testing, orthogonal block structure, proper block designs, randomization-derived model
