Statistical efficiency of incomplete block designs over complete block designs in agriculture: A review

Abstract:

Field experimentation forms the backbone of agricultural research, enabling scientists to evaluate treatments under realistic growing conditions. However, soil heterogeneity remains a primary source of experimental error, reducing the precision and reliability of results. This review comprehensively examines the statistical efficiency of Incomplete Block Designs (IBDs) including Balanced Incomplete Block Design (BIBD), Partially Balanced Incomplete Block Design (PBIBD), Alpha Lattice Design (ALD), Variance Balanced Design (VBD), Lattice Designs and Augmented Designs in comparison with Complete Block Designs such as CRD, RCBD, LSD and Split Plot Design. Evidence from nine case studies across crops including wheat, brinjal, oat, triticale and durum wheat consistently demonstrates the superiority of IBDs. Relative efficiency values ranged from 17% (4×4 square lattice) to over 147% (Alpha Lattice vs. RCBD in durum wheat) and up to 233% (VBD vs. RCBD in brinjal). VBD demonstrated the highest average efficiency gain of 58.06% over RCBD, while ALD averaged 30.74%. These findings advocate for the wider adoption of IBDs in agricultural field research.