Additive design: the concept and data analysis

Summary Crop–weed competition is extensively studied in weed science. The additive design, in which weed density varies and the crop density is kept constant, is the most commonly utilised design in plant competition studies. The additive design is important to calculate economic weed thresholds and improve weed control decision‐making. Crop–weed competition studies are usually conducted by weed scientists, who sometimes report misleading conclusions because of lack of statistical knowledge needed for data analysis of such studies. Therefore, the objective of this manuscript is to provide the concept of additive design and demonstrate the model selection approach for describing crop–weed density relationship to non‐statisticians. We evaluated three models routinely used in the literature to interpret data from additive designs, including polynomial quadratic, sigmoid and rectangular hyperbola curves. Based on the described statistical criteria, we demonstrated the rectangular hyperbola to be the most appropriate model to describe data from an additive design study looking at Richardia brasiliensis and Commelina benghalensis competition with maize ( Zea mays ). Moreover, we describe step‐by‐step how to perform the statistical analysis in R software and interpret the results of crop–weed competition studies. We suggest the use of the rectangular hyperbola as a standardised model for crop–weed competition in additive design.