2025, Vol. 10, Special Issue 8

Factorial experimental design serves as a fundamental statistical framework for evaluating the effects of multiple factors, their levels, and the interactions between them. When standard assumptions are met, traditional analysis of variance (ANOVA) is typically used. However, when these assumptions are violated-such as in the presence of non-normality or heteroscedasticity-alternative estimation methods become necessary. This study examines the comparative efficiency of various estimation techniques, including Ordinary Least Squares (OLS), Generalized Linear Models (GLM), Quantile Regression, the Least Absolute Shrinkage and Selection Operator (LASSO), Adaptive LASSO, and the MM-estimator. The research focuses on assessing the robustness of each method to outliers, the accuracy of estimating main and interaction effects, and the flexibility of handling complex factorial designs (specifically 23 structures), under challenging data conditions often encountered in agricultural experiments. Additionally, the study explores the role of data transformation techniques, model selection criteria, and diagnostic tools in improving the reliability of statistical analysis. Comparative evaluations are conducted across varying sample sizes, effect sizes, and error distributions to reflect a wide range of experimental scenarios. The overarching goal is to provide agricultural researchers with practical, evidence-based guidance for selecting appropriate statistical methodologies in factorial experiments, thereby enhancing the validity and interpretability of their results.