The observation of coherent elastic neutrino nucleus scattering (CEνNS) by the COHERENT collaboration in 2017 has opened a new window to both test StandardModel predictions at relatively low energies and probe new physics scenarios. Our investi-gations show, however, that a careful treatment of the statistical methods used to analyzethe data is essential to derive correct constraints and bounds on new physics parameters.In this manuscript we perform a detailed analysis of the publicly available COHERENTCsI data making use of all available background data. We point out that due to the lowstatistics of the CsI data, Wilks’ theorem is not fulfilled in general and a calculation of theconfidence regions via Monte Carlo simulations following a Feldman-Cousins procedure isnecessary. As an example for the necessity of this approach to test new physics scenarios wequantify the allowed ranges for several scenarios with neutrino non-standard interactions.We emphasize the effect of binning which can change the constraints if incorrectly applied.Furthermore, we provide accompanying code to enable an easy implementation of othernew physics scenarios as well as data files of our results.