ON BLOCK DESIGNS FOR COMPARING TEST TREATMENTS WITH CONTROL(S)
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Date
2018
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ICAR-INDIAN AGRICULTURAL STATISTICS RESEARCH INSTITUTE ICAR-INDIAN AGRICULTURAL RESEARCH INSTITUTE
Abstract
There are many research investigations where the interest of the experimenter is in
comparing a set of new treatments called test treatments with one or more established
standard treatment(s) known as control treatment(s). Under the presence of one nuisance
factor, two popular classes of block designs for comparing test treatments with control
treatment(s) namely balanced treatment incomplete block (BTIB) designs and balanced
bipartite block (BBPB) designs are used for such situations.
In this investigation, two new classes of block designs namely nearly balanced treatment
incomplete block (nearly BTIB) designs and nearly balanced bipartite block (nearly
BBPB) designs are introduced for comparing test treatments with a single control
treatment and with more than one control treatments, respectively. Necessary parametric
conditions for existence of these two classes of block designs are obtained. Two
algorithms are proposed to construct nearly BTIB and nearly BBPB designs for given
parameters. The algorithms are implemented using R programming language. Nearly
BTIB designs are obtained in a restricted parametric range using the first algorithm. In the
restricted parametric range, a total of 635 nearly designs are possible and 618 of them are
constructed. It was found that 198 nearly BTIB designs have higher A-efficiency
compared to BTIB designs of Mandal et al. (2013). Using the second algorithm, nearly
BBPB designs are also obtained in a restricted parametric range. In this parametric range,
886 nearly BBPB designs may exist out of which 874 designs are obtained.
Description
t-9896
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