Much of the absolute differential cross-section data for elastic scattering by 3He depends on an experiment at the Los Alamos National Laboratory (LANL), published in 1974. Since that time, computer techniques have been developed that can make more accurate corrections for, e.g., sample-size effects. Since complete documentation of the LANL experiment is available, modern analysis techniques were applied to improve these data, based on simulations using the Los Alamos Monte Carlo neutron transport code MCNPX. Of a total of 29 published differential cross-section distributions, 15 published in 1982 from another laboratory depend on the LANL data but were not corrected for sample-size effects and therefore provide only relative yield functions. The present study simulates these latter data using MCNPX to obtain self-attenuation correction factors for the scattered neutrons. An energy-dependent analysis shows that at neutron energies between 5 and 14 MeV, these latter corrected data are in good agreement with the other data, whereas above 22 MeV they are not. A complete energy-dependent analysis of all absolute differential cross sections between 5 and 23.7 MeV is presented.