A rigorous statistical approach is presented to address the shortcomings inherent in the analysis of counting experiments such as orbital neutron spectroscopy endeavors. Unlike the quasi-Gaussian statistics commonly applied to such investigations, the methodology described here incorporates fundamental elements of Poisson statistics including its inherent nature as a bounded, discrete, and intrinsically asymmetric probability distribution. In addition, we utilize the proper statistical formulae required to describe the data following background subtraction. Utilizing the Likelihood Ratio Method for hypothesis testing, we find that analyses utilizing collimated instruments such as the Lunar Exploration Neutron Detector (LEND) aboard NASA's Lunar Reconnaissance Orbiter overestimate detection significances by , under the assumption that collimator effectiveness as asserted by the LEND team is correct. This in turn implies that the required exposure times must be ∼2× longer to reach prelaunch sensitivity estimates. We provide updated estimates for hydrogen abundance sensitivity limits as a function of exposure time and compare the sensitivities of collimated (i.e., background subtracted) and uncollimated approaches.