COMPONENTS

The research work explores the comparison of various methods for estimating variance components in a two-way random effects model, a critical task in experimental data analysis. The methods assessed include classical Analysis of Variance (ANOVA), Restricted Maximum Likelihood (REML), and Bayesian estimation. The experiment was designed with treatments (3 levels) and blocks (4 levels), with each combination replicated 5 times, resulting in 60 observations. The objective was to estimate variance components attributable to treatments, blocks, and errors. The results were compared across the three methods: ANOVA produced variance components of σ²α = 3.84, σ²β = 2.43, and σ²ε = 3.58, while REML and Bayesian estimates were σ²α = 4.805 and 4.75, σ²β = 2.4067 and 2.60, and σ²ε = 3.58 and 3.60, respectively. While the three methods yielded similar results, minor differences were observed, reflecting their respective properties. ANOVA, though simple and interpretable, may be biased in small samples or unbalanced designs, whereas REML offers better performance in such situations, and Bayesian estimation provides flexibility with credible intervals to quantify uncertainty. The research work highlights the importance of method selection depending on sample size, design, and the need for uncertainty quantification, suggesting future work on more complex or larger-scale experiments.