Toward a standardized statistical methodology comparing optimum nitrogen rates among management practices: A bootstrapping approach

There are a range of approaches to compare differences between or among optimum nitrogen (N) fertilizer rates resulting from different management practices; however, this goal lacks statistical standardization. To provide the statistical rigor needed to give clear recommendations for greater or less N need based on specific management practices, we propose a bootstrapping approach that resamples residuals with replacement. While bootstrapping is not new to data processing in agronomic fields, we provide an example of how to conduct residual-resampled bootstrapping with nonlinear regression to identify differences in response curves, optimum N rates, and maximum yields using the FertBoot package in R. Our example dataset provides clear evidence of the value of the bootstrapping approach, as it can aid in determining significant differences between even relatively small differences in optimum N rate. We encourage adoption of this approach as a way to accurately evaluate differences in optimum fertilizer levels between or among treatments to better inform future agronomic decision making.