~33~ International Journal of Statistics and Applied Mathematics 2024; 9(1): 33-38 ISSN: 2456-1452 Maths 2024; 9(1): 33-38 © 2024 Stats & Maths https://www.mathsjournal.com Received: 18-11-2023 Accepted: 25-12-2023 B Manjunatha ICAR-Indian Agricultural Statistics Research Institute, Pusa, New Delhi, India Rajender Parsad ICAR-Indian Agricultural Statistics Research Institute, Pusa, New Delhi, India BN Mandal ICAR-Indian Agricultural Research Institute, Jharkhand, India Sukanta Dash ICAR-Indian Agricultural Statistics Research Institute, Pusa, New Delhi, India Vinayaka ICAR-Sugarcane Breeding Institute, Coimbatore, Tamil Nadu, India Corresponding Author: B Manjunatha ICAR-Indian Agricultural Statistics Research Institute, Pusa, New Delhi, India Construction of structurally incomplete row-column designs for comparing test treatments with control treatments B Manjunatha, Rajender Parsad, BN Mandal, Sukanta Dash and Vinayaka DOI: https://dx.doi.org/10.22271/maths.2024.v9.i1a.1573 Abstract In this paper, construction methods to obtain structurally incomplete row-column designs for comparing test treatments with control treatments which includes structurally incomplete Balanced Treatment - Control Row-Column (BTRC) design and structurally incomplete Balanced Bipartite Row-Column (BBPRC) designs for experimental situations where the experimenter is interested only in a subset of comparisons like in comparing several new treatments, called test treatments with existing (standard) treatment(s), called control treatment(s). For a ready reckoner, the catalogues of structurally incomplete BTRC and BBPRC designs obtainable from the given methods of construction for v1 (number of test treatments), b1 (number of rows), b2 (number of columns), k1 (number of non-empty nodes in rows) and k2 (number of non-empty nodes in columns), r (number of replications of test treatments)  15 and r 0 (number of replications of control treatments)  30 have been prepared. Keywords: Structurally incomplete row-column designs, test treatments, control treatments, balanced bipartite row-column designs, balanced treatment - control row-column designs 1. Introduction Row-column designs are used in experimental situations when the heterogeneity in the experimental material is in two direction. In row-column design experiments, there may be situations in which the experimenter interested in comparing a set of test treatments with control treatments with unequal replication between the test treatments and control treatments, due to more number of treatments, one may have to conduct the experiment in incomplete rows or columns. For such experimental situations, structurally incomplete row-column designs for comparing test treatments with control treatments which includes structurally incomplete Balanced Treatment - Control Row-Column (BTRC) design and structurally incomplete Balanced Bipartite Row-Column (BBPRC) designs were useful. The research work related to BTRC and BBPRC designs for making comparisons of several test treatments with one or two control treatments, Ture [7] introduced balanced treatment row- column (BTRC) designs for multiple comparisons with a control. Parsad and Gupta [4] introduced a new design class called balanced bipartite row-column (BBPRC) designs to compare test treatments with more than one control treatment. Parsad et al. [5] also provided a structurally incomplete row-column design method for comparing test treatments with control treatment(s). Sarkar et al. [6] gave some general methods of construction of BTRC designs in complete/incomplete rows/columns. In the present investigation, methods of construction for obtaining structurally incomplete BTRC and BBPRC designs for comparing test treatments with one or two control treatment(s) are provided. The catalogues of these designs obtainable from given methods of construction for v1 (number of test treatments), b1 (number of rows), b2 (number of columns), k1 (number of non-empty nodes in rows) and k2 (number of non-empty nodes in columns) ≤ 15 r (number of replications of test treatments)  15 and r 0 (number of replications of control treatments)  30 are presented in Appendix.