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Block designs and electrical networks. (English) Zbl 0725.62066

Summary: For a given block design, an electrical network is constructed in which blocks and treatments are represented by points and observations by connections. This network has the property that the resistance between two points representing two different treatments is equal to the variance on the estimate of the corresponding treatment contrast in the usual additive block effect plus treatment effect model. This provides a simple tool for computation of contrast variances in many examples.
Further, applications are made to obtain lower bounds for contrast variances and upper bounds for efficiencies. A particular application is a complete solution to the problem of finding the A-optimal design in the case where the number of blocks equals the number of treatments and the blocks are of size 2.

MSC:

62K10 Statistical block designs
94C30 Applications of design theory to circuits and networks
62K05 Optimal statistical designs
94C15 Applications of graph theory to circuits and networks
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