On The Construction And Evaluation Of Nine-Treatment Incomplete-Block Designs Of Order Three From Some Quasi-Semi-Latin Squares
DOI:
https://doi.org/10.60787/tnamp.v21.507Keywords:
Block Structure, Canonical Efficiency, Pairwise Efficiency, Optimality criteria, Simple ContrastAbstract
The efficiency and optimality characterization of eight incomplete-block designs from some quasi-semi-Latin squares of order three were evaluated in this study. The quasi-semi-Latin squares were constructed from three distinct and unique quasi-semi-Latin squares. Incomplete-block designs were generated from the quasi-semi-Latin squares by considering different block structures: ‘short’ rows, ‘little’ columns and alternate treatment positions. The variance of the treatment contrasts, , , show that design is near-variance-balanced. Treatment pairs estimated with the same variance have the same efficiency while treatment pairs with minimum variances are the most efficient. The designs, , and , constructed using “little” columns as blocks have the same A-, D-, E- and MV-optimality criteria. The IBDs constructed using “little” columns as blocks led to about 8 % loss of information while the designs constructed using “short” rows as blocks led to about 39 % loss of information
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