Estimation of optimal plot size for chickpea experiments using Bayesian approach with prior information

Abstract

Heterogeneity among experimental units can introduce experimental errors, necessitating the use of techniques that enhance statistical inferences to address this issue. One effective approach is determining the optimal plot size, which can reduce experimental error. While frequentist methods are commonly employed for this purpose, Bayesian approaches offer distinct advantages. Therefore, our objective was to estimate the optimal plot size for chickpea experiments using the Bayesian approach and compare the results with those from the frequentist approach. We conducted two control experiments (with no treatments) involving eight cultivation rows, each spanning seven meters in length, with 50 cm spacing between rows and 10 cm spacing between plants. We evaluated the central six rows, totaling 60 plants per cultivation row. At the end of the growth cycle, we assessed seed count, seed weight, harvest index, and shoot dry mass. Data collection was conducted at the individual plant level. We determined the optimal number of plots using both the frequentist approach (modified maximum curvature method) and Bayesian approach, employing informative and uninformative prior distributions. The optimal plot size varied depending on the specific experiments and the variables under analysis. However, there was consensus in the estimation of the optimal experimental plot size between the two approaches. We recommend using 15 plants as the optimal plot size for chickpea cultivation.

Keywords

• Cicer arietinum; agricultural experimentation; legume; Bayes’ theorem.