Combined Analysis of Orthogonal Nested Row-Column Design
Agbana A. A.
Dauran N.S.
Almu A.
Abstract
Traditional experimental designs, including the recent Orthogonal Nested Row-Column (NRC) design, are only applicable for single-environment experiments. They fail to provide a unified framework for the combined analysis of identical experiments conducted across multiple environments (e.g., different locations or seasons). This gap prevents a rigorous investigation of critical Treatment-by-Environment interactions and leads to a loss of statistical power and information. This study proposes a new Combined Orthogonal Nested Row-Column (ONRC) design that integrates environment effects and their interactions into the linear model. The methodology involved the derivation of the sums of squares and the construction of a unified ANOVA table for this combined analysis. Specifically, the ONRC model assumes independent randomizations of blocks, rows, and columns within environments, employs a linear mixed-model framework with orthogonal block structures, and analyzes data derived from multi-environment yield trials using direct ANOVA decomposition across six strata.Results from a hypothetical case study show the ONRC design significantly reduces experimental error and achieves higher relative efficiency compared to the existing NRC design, confirming its superiority for accurate multi-environmental trials. Quantitatively, the ONRC design reduced mean square error from 3.41 (NRC) to 0.92 and improved relative efficiency by approximately 270%, demonstrating substantial gains in precision and accuracy. The study concludes that the proposed Combined Orthogonal Nested Row-Column (ONRC) design is a more efficient and powerful design than its predecessors. The research recommends the use of the ONRC design for agricultural and industrial experiments conducted across multiple locations and suggests future work to extend the model to factorial treatment structures.
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