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Interblock information in multidimensional block designs
Author(s) -
Stewart Frances P.,
Bradley Ralph A.
Publication year - 1993
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315755
Subject(s) - blocking (statistics) , estimator , block (permutation group theory) , computer science , basis (linear algebra) , variance (accounting) , class (philosophy) , random effects model , variance components , adaptation (eye) , algorithm , mathematical optimization , theoretical computer science , statistics , mathematics , artificial intelligence , combinatorics , medicine , meta analysis , geometry , accounting , business , computer network , physics , optics
In many experimental situations, d ‐way heterogeneity among experimental units may be controlled through use of multiple blocking criteria. In some cases it is reasonable to regard some or all of the block effects as random. Then the model is mixed and observations within blocks are correlated. Very general estimators of treatment effects and their dispersion matrix with recovery of interblock information are provided. They apply to designs with d > 1 blocking criteria that may be crossed, nested, or a combination thereof. These general results may be specialized to provide analyses of new classes of MBD's or used directly for numerical analyses of designs in the general class, perhaps through use as the basis for very general computer programs. Estimation of variance components is discussed, and an example is provided to illustrate adaptation of the general results.