Analyzing Efficiency in Regular-Graph Semi-Latin Rectangles With Block Size Two and Odd Treatments

A semi-Latin rectangle (SLR), denoted (h × p)/k, is a row-column design consisting of v treatments in h rows and p columns (where h may or may not be equal to p), where each row-column intersection (cell) which constitutes a block contains k treatments and each treatment of the design occurs the same number of times in each row, denoted 𝑛𝑟 and the same number of times in each column, denoted 𝑛𝑐 (where 𝑛𝑟 and 𝑛𝑐 need not be all 1). Regulargraph semi-Latin rectangles (RGSLRs) are SLRs which possess the property that, for any two pairs of distinct treatments, their concurrences differ by at most one. This work considers RGSLRs with k = 2, where the number of treatments (v) is odd and h = p = v, which are the smallest RGSLRs for odd values of v. Construction for such design is given in Uto and Bailey (2022). However, the foregoing paper does not give the efficiency measures of these designs. We determine the A-, D- and E-efficiency measures of these designs for some odd values of v to give information on how good the designs are for experimentation. Results show that the designs have good efficiency measures, hence are good designs for experiments involving designs of their sizes.