Listy Biometryczne - Biometrical Letters Vol. 31(1994), No. 2, 45-77
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ON THE RANDOMIZATION THEORY OF EXPERIMENTS IN NESTED BLOCK DESIGNS Tadeusz Caliński Department of Mathematical and Statistical Methods, Agricultural University of Poznań, Wojska Polskiego 28, 60-637 Poznań, Poland |
A general randomization model for experiments in nested block designs is presented and conditions are given for obtaining the best linear unbiased estimators under the model. Since the conditions appear to be severely restrictive, a resolution of the overall randomization model into four relevant stratum submodels is considered. Conditions for obtaining the best linear unbiased estimators under these submodels are found. In addition, it is shown under which conditions the best linear unbiased estimator for a treatment parametric function obtainable under a submodel becomes such an estimator under the overall model. Two discussed examples illustrate application of the theory. Finally, some general concluding remarks complete the paper.
best linear unbiased estimation, nested block designs, intra-block analysis, inter-block-intra-superblock analysis, inter-superblock analysis, randomization model
