On The Construction And Evaluation Of Nine-Treatment Incomplete-Block Designs Of Order Three From Some Quasi-Semi-Latin Squares

Authors

  • Livinus N. Ogbonna Department of Mathematics and Applied Statistics, Ebonyi State University, Ebonyi State, Nigeria Author
  • Chiemeka N. Okoro Department of Mathematics and Applied Statistics, Ebonyi State University, Ebonyi State, Nigeria Author
  • U. A. Osisiogu Department of Mathematics and Applied Statistics, Ebonyi State University, Ebonyi State, Nigeria Author
  • Eugene C. Ukaegbu Faculty of Natural and Applied Sciences, State University of Medical and Applied Sciences, Igbo-Eno, Enugu State, Nigeria Author

DOI:

https://doi.org/10.60787/tnamp.v21.507

Keywords:

Block Structure, Canonical Efficiency, Pairwise Efficiency, Optimality criteria, Simple Contrast

Abstract

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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Published

2025-05-01

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How to Cite

On The Construction And Evaluation Of Nine-Treatment Incomplete-Block Designs Of Order Three From Some Quasi-Semi-Latin Squares. (2025). The Transactions of the Nigerian Association of Mathematical Physics, 21. https://doi.org/10.60787/tnamp.v21.507

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