We discuss the impact of strong absorption for thermal neutrons on data analysis and compare absorption corrections in the GSAS and MAUD Rietveld codes for texture and structural parameter refinement. Diffraction data were collected on the neutron powder diffractometer HIPPO at LANSCE from dysprosium and erbium, which are moderate-to-strong absorbers for thermal neutrons with absorption cross sections of 159 barns for Er and 994 barns for Dy at λ=1.8 Å. Both elements have hexagonal-close-packed (hcp) crystal structures, and the samples were various thicknesses of rolled foils. The orientation distribution functions (ODF) were fit to the same neutron time-of-flight data sets using two very different full pattern Rietveld analysis procedures. Spherical harmonics functions were fit to the textured data using GSAS. These data were also analyzed by the modified direct method E-WIMV using MAUD. The resulting pole figures from the ODFs determined by both Rietveld analysis packages are qualitatively similar, and the textures were confirmed by X-ray diffraction. Additionally, data from orthorhombic dysprosium and erbium fluoride powders show that atomic positions are not sensitive to absorption. We address inconsistencies and methodologies in data analysis when strong absorption is present.