Biometrical Letters Vol. 55(2), 2018, pp. 147-178
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ON A NEW APPROACH TO THE ANALYSIS OF VARIANCE FOR EXPERIMENTS WITH ORTHOGONAL BLOCK STRUCTURE. II. EXPERIMENTS IN NESTED BLOCK DESIGNS Tadeusz Caliński, 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 procedures are presented for experiments conducted in nested block designs of a certain type. It is shown that, under appropriate randomization, these experiments have the convenient orthogonal block structure. Due to this property, the analysis of experimental data can be performed in a comparatively simple way. Certain simplifying procedures are indicated. The main advantage of the presented methodology concerns the analysis of variance and related hypothesis testing procedures. Under the adopted approach one can perform these analytical methods directly, not by combining the results from analyses based on stratum submodels. The application of the presented theory is illustrated by three examples of real experiments in relevant nested block designs. The present paper is the second in the planned series concerning the analysis of experiments with orthogonal block structure.
analysis of variance, estimation, hypothesis testing, nested block designs, orthogonal block structure, randomization-derived model
