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THE ANALYSIS OF MULTISTRATA DESIGNED EXPERIMENTS WITH INCOMPLETE DATA
Author(s) -
Houtman A.,
Speed T.P.,
Nielsen A. C.
Publication year - 1984
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1984.tb00446.x
Subject(s) - mathematics , simple (philosophy) , lattice (music) , computer science , matrix (chemical analysis) , algorithm , block (permutation group theory) , covariance , statistics , combinatorics , philosophy , physics , materials science , epistemology , acoustics , composite material
summary Building upon early work of E. A. Cornish we show that G. N. Wilkinson's version of Yates' approach to the analysis of designed experiments with a single error stratum carries over completely to designs with an arbitrary non‐singular covariance matrix, initially assumed known. We show that the equations, corrections, adjustments and algorithms all have their more general analogues and that these can be solved, computed or executed quite readily if the design has orthogonal block structure and satisfies Nelder's condition of general balance. The results are illustrated with a split‐plot and a simple (square) lattice design.