Trend‐Free Nested Balanced Incomplete Block Designs and Designs for Diallel Cross Experiments

Abstract

Abstract: Nested balanced incomplete block (NBIB) designs are useful when the experiments are conducted to deal with experimental situations when one nuisance factor is nested within the blocking factor. Similar to block designs, trend may exist in experimental units within sub‐blocks or within blocks in NBIB designs over time or space. A necessary and sufficient condition, for a nested block design to be trend‐free at sub‐block level, is derived. Families and catalogues of NBIB designs that can be converted into trend‐free NBIB designs at sub‐block and block levels have been obtained. A NBIB design with sub‐block size 2 has a one to one correspondence with designs for diallel crosses experiments. Therefore, optimal block designs for dialled cross experiments have been identified to check if these can be converted in to trend‐free optimal block designs for diallel cross experiments. A catalogue of such designs is also obtained. Trend‐free design is illustrated with example for a NBIB design and a design for diallel crosses experiments. AMS (2000) Subject Classification: 62K05, 62K10.