Bayesian determination of the number of replications in crop trials

Abstract

The number of replications required in a particular experiment depends on the magnitude of difference intended for detection and the inherent error variability in the response. This paper describes Bayesian approach for determination of the number of replications, based on prior information on heterogeneity in experimental fields in terms of coefficient of variation (CV) on lentil seed yield. The distribution of observed CV was found to be a shifted log-normal distribution taken as prior information. For such a distribution, the Bayesian value was obtained as a function of an assumed ratio of variances of prior distributions of the means. The number of replications, under the Bayesian methods, declined with the ratio. Further, the replication increased with the observed level of heterogeneity. For CV less than 16%, the frequentist value for number of replications were less than those under the Bayesian, while above that level the trend was reversed