Construction of Partially Balanced Semi-Latin   Rectangles with Block Size 4

Kaushal Kumar Yadav; Sukanta Dash; Rajender Parsad; Baidya Nath Mandal; Anil Kumar; Mukesh Kumar

doi:10.56093/jisas.v78i02.171354

Authors

Kaushal Kumar Yadav The Graduate School, ICAR-Indian Agricultural Research Institute, New Delhi
Sukanta Dash ICAR-Indian Agricultural Statistics Research Institute, New Delhi
Rajender Parsad ICAR-Indian Agricultural Statistics Research Institute, New Delhi
Baidya Nath Mandal ICAR-IARI, Gauria Karma, Jharkhand
Anil Kumar Indian Council of Agricultural Research, New Delhi
Mukesh Kumar ICAR-Indian Agricultural Statistics Research Institute, New Delhi

https://doi.org/10.56093/jisas.v78i02.171354

Keywords:

Semi Latin Rectangle; Partially Balanced Semi-Latin rectangles; Canonical efficiency factor; Average efficiency factor.

Abstract

Semi-Latin rectangles represent row-column designs where each row-column intersection contains the same number of experimental units, denoted as 1 k . Additionally, each treatment appears an equal number of times in each row ( r , say) and in each column ( c may
or may not be same). Partially Balanced Semi-Latin rectangles (PBSLR) constitute a subset of Semi-Latin rectangles (SLR), serving as generalizations , say) ( 1 r n and 1 c n of Latin squares and Semi-Latin squares (SLS). These designs find utility in various agricultural and industrial experiments, particularly situations where one effect is considered a column effect and the other a row effect, with the intersection (block/cell) accommodating precisely four units. This article introduces two methods for constructing PBSLR designs with a block size of 4. Also, R package has been developed for generating the designs.

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