Robustness and Efficiency of Complete versus Balanced Incomplete Sudoku Square Designs: A Comparative Study
Dauran N. S.
Ibrahim Muhammad
Abdulaziz Shehu
Haliru Haliru
Abstract
Researchers in industrial engineering, agriculture, and pharmaceutical sciences require evidence-based guidance when selecting experimental designs that optimally balance precision, cost, and feasibility. While Complete Sudoku Square Designs (CSSDs) guarantee full treatment balance, they often require a large number of experimental runs. In contrast, Balanced Incomplete Sudoku Square Designs (BISSDs) reduce experimental burden by sacrificing partial completeness, yet the statistical implications of this trade-off remain insufficiently explored. Although previous studies have focused on the construction and analysis of CSSD and BISSD, their relative efficiency and robustness have not been adequately investigated. This study presents a comparative assessment of the statistical efficiency and robustness of CSSD and BISSD using three performance criteria: mean squared error (MSE), p-values associated with treatment effects, and the power of the F-test. Both hypothetical experimental data and Monte Carlo simulation techniques were employed for evaluation. The results indicate that CSSD consistently outperforms BISSD across all criteria, with relative efficiency values exceeding unity. Although both designs remain suitable for experiments requiring row–column–block balance, CSSD demonstrates superior precision and robustness, while BISSD offers greater flexibility when experimental resources are constrained. These findings provide practical guidance for researchers in selecting appropriate Sudoku-based experimental designs.
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