A Bayesian inference for treatment effects in randomized block design

This paper presents a Bayesian analysis of the effect of organic spray treatment on the yield of Amaranthus dubius, a leafy vegetable of significant nutrition value. Given the increasing demand for sustainable agricultural practices, this research aims to provide a Bayesian perspective for the analysis of variance (ANOVA) of organic interventions. The Bayesian approach facilitated the incorporation of prior knowledge and the quantification of uncertainty in yield predictions. In the place of frequentist ANOVA including the Bayesian may include the prior knowledge by the given data and result in precise conclusions. A randomized controlled trial involving four replications was conducted to compare yields from plots subjected to 6 different organic spray treatments and one non- organic spray treatment (urea - for reference) against control plots with no treatment. Modelling was conducted using the R programming language, employing packages such as brms and rstan to fit hierarchical models that account for variability across treatments and environmental conditions. Findings revealed a statistically significant increase in yield associated with the organic spray treatment, with credible intervals indicating substantial effect sizes. Model diagnostics, including posterior predictive checks, confirmed the adequacy of the model fit. The application of Bayesian methods provides a comprehensive statistical approach to assess the impact of organic treatments, offering valuable insights for future agricultural research-like advanced factorial, balanced designs and practice.