A Practical Guide to Statistical Techniques in Particle Physics

Abstract: In high-energy physics (HEP), both the exclusion and discovery of new theories depend not only on the acquisition of high-quality experimental data but also on the rigorous application of statistical methods. These methods provide probabilistic criteria (such as p-values) to compare experimental data with theoretical models, aiming to describe the data as accurately as possible. Hypothesis testing plays a central role in this process, as it enables comparisons between established theories and potential new explanations for the observed data. This report reviews key statistical methods currently employed in particle physics, using synthetic data and numerical comparisons to illustrate the concepts in a clear and accessible way. Our results highlight the practical significance of these statistical tools in enhancing the experimental sensitivity and model exclusion capabilities in HEP. All numerical results are estimated using Python and RooFit, a high-level statistical modeling package used by the ATLAS and CMS collaborations at CERN to model and report results from experimental data.