In general there is a systematic error in the results of any in-beam neutron absorption experiment because of neutron scattering in the sample. The error is largest when scattering predominates over absorption, when the transmission of the sample is small, and when the lateral dimensions of the sample are large compared with its thickness. The ratio of the reaction rate in the sample, to the rate calculated ignoring both scattering and self-shielding due to absorption, may be significantly less than or greater than unity, depending on the scattering properties of the sample and its size and shape. These conclusions are derived from Monte Carlo calculations based on a very general expression for the rate of a neutron absorption reaction in a sample which scatters and absorbs neutrons. The expression for the reaction rate, written as a sum over orders of scattering within the sample, was obtained using the technique adopted by V.F. Sears [Adv. Phys. 24 (1975) 1] in his study of multiple scattering effects in neutron scattering experiments. Our calculations were performed for slab samples placed in a narrow, monoenergetic, monodirectional neutron beam. The assumed scattering cross section was isotropic and also static, meaning that no change in neutron energy was permitted to occur within the sample. This work has potentially important implications in various areas of neutron research including activation analysis and radiography.