Estimating and Testing Augmented Randomized Complete Block Designs: The Neutrosophic Approach

In plant breeding programs, the augmented design is designated to screen numerous new treatments compared with a few check treatments, which in turn are required to estimate both of error variance and local control for new future treatments. It is well known that the classical augmented design is not suitable for data that are imprecise, uncertain, or undetermined, and these accordingly emerge because of many circumstances beyond humans control. As a result, there is a sever necessity to define a proper generalization for the augmented designs to handle uncertain environments. To be more specific, this work aims to propose an easy to apply approach to treat the augmented randomized complete block design under neutrosophic statistics (NS). This well-defined approach is based on building a neutrosophic ANOVA table, including deriving a suitable test statistics, FN , to handle uncertain settings.This leads to the corresponding neutrosophic hypotheses and the necessary related decision rules. Real data and a series of simulation studies numerically assess the performance of the present method. It will be shown that the neutrosophic method outperforms the classical one, and in effect, it is more flexible than in the presence of indeterminacy.