Efficient block designs for comparing test treatments to a control when the errors are correlated
Copyright policy )Efficient block designs for comparing test treatments to a control when the errors are correlated
The problem of comparing test treatments with a control or mainly standard treatments has been dealt with. The author considered the efficient circular neighbour balanced treatment incomplete block (CNBTIB) designs and its subfamily. The main feature of the paper is that it presupposes an autoregressive correlation structure. Use of the information matrix for treatment effects and treatment-control contrasts has been extensively made. A condition for CNBTIB designs to be the best under the \(A\)-optimality criterion has been derived. Efficiencies of best CNBTIB for different correlation coefficient values and number of treatments have been calculated. The author has also considered rectangular block designs which lead to augmented neighbour balanced incomplete block designs. These designs are also proved to be \(A\)-optimal. He has proved a number of theorems and lemmas required to prove the optimality of the efficient block designs.
- Utah State University United States
rectangular block designs, rectangular designs, autoregressive correlation structure, \(A\)-optimality, Statistical block designs, circular designs, efficient circular neighbour balanced treatment incomplete block designs, comparing test treatments to a control, stationary, first order autoregressive correlation structure, comparing test treatments with a control, treatment-control contrasts, Optimal statistical designs, BIB designs, information matrix, general optimality theorems, construction of designs, ANBIB designs, incomplete blocks, \(A\)- optimality, phi-optimality, CNBTIB designs
rectangular block designs, rectangular designs, autoregressive correlation structure, \(A\)-optimality, Statistical block designs, circular designs, efficient circular neighbour balanced treatment incomplete block designs, comparing test treatments to a control, stationary, first order autoregressive correlation structure, comparing test treatments with a control, treatment-control contrasts, Optimal statistical designs, BIB designs, information matrix, general optimality theorems, construction of designs, ANBIB designs, incomplete blocks, \(A\)- optimality, phi-optimality, CNBTIB designs
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