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Bhartiya Krishi Anusandhan Patrika

Partially Balanced 3-Designs using Mutually Orthogonal Latin Squares

DOI: 10.18805/BKAP351    | Article Id: BKAP351 | Page : 8-12
Citation :- Partially Balanced 3-Designs using Mutually Orthogonal Latin Squares.Bhartiya Krishi Anusandhan Patrika.2022.(37): 8-12
Sayantani Karmakar, Cini Varghese, Seema Jaggi, Mohd Harun, Devendra Kumar mohd.harun@icar.gov.in
Address : ICAR-Indian Agricultural Statistics Research Institute, Pusa-110 012, New Delhi, India.
Submitted Date : 9-08-2021
Accepted Date : 12-03-2022
First Online:

Abstract

t-designs represent a generalized class of balanced incomplete block designs in which the number of blocks in which any t treatments (t ≥ 2) occur together is a constant. Like other families of incomplete block designs, t-designs find potential application in farming system research where the main concern would be to select the best combination out of a certain set of t-component farming systems for a specific agro-ecological zone. But in order to obtain t-balance we may require large number of blocks and replications. Partially balanced t-designs are introduced for experimental situations where it is not possible to get t-balanced designs. A series of partially balanced 3-designs are constructed using mutually orthogonal Latin Squares. These designs, though possess pair-wise balance, are not combinatorially balanced in terms of 3-tuples. They also satisfy the properties of 3-packing designs. The efficiency factor of these designs is quite high as v increases, the efficiency increases.

Keywords

Balanced incomplete block designs Canonical efficiency factor Mutually orthogonal latin squares t-packing

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