In applied sciences, an experiment is defined by a parameter setting, and it leads to an associated outcome. For example, when carried out under different conditions, a chemical reaction leads to different yields. Finding a satisfactory outcome is a difficult task when the number of possible settings is too large: it becomes unfeasible to explore all the possibilities due to material and time constraints. It is therefore important to quickly identify a setting that leads to a sufficient enough outcome. Bayesian optimization offers a strategy to efficiently explore parameter settings. However, the latter needs to be improved to identify interesting settings earlier. Our contribution, BOWSA, analyzes the outputs of Bayesian optimization through sensitivity analysis: it quantifies the association between each parameter and the outcome. Then, BOWSA uses this information to generate a score that refines the outputs of the Bayesian optimization. This paper provides a methodological description of BOWSA. It proposes an implementation that uses the existing EDBO, Experimental Design via Bayesian Optimization tool, a practical implementation of Bayesian optimization designed to handle both discrete and categorical inputs, making it particularly well-suited for experimental science applications. An evaluation has been conducted on several datasets derived from well-known functions and two chemical synthesis reactions from the EDBO repository. Comparative results demonstrate that on average, BOWSA identifies productive settings earlier than Bayesian optimization alone.