Polarized Raman Spectroscopy (PRS) is used to quantify the orientational order in the conventional (N) and twist-bend (N_TB) nematic phases of a homologous series of liquid crystalline dimers. The dimers investigated have 7, 8, 9 and 11 methylene groups connecting two cyanobiphenyl mesogens and data for 4-pentyl-4′-cyanobiphenyl (5CB) and 4-octyl-4′-cyanobiphenyl (8CB) are included for comparison. Simulated and measured Raman spectra for the materials are compared. PRS is used to determine both 〈P₂〉 and 〈P₄〉 order parameters across the nematic temperature range and immediately below the N_TB–N phase transition using a model that takes into account the molecular bend of the odd dimers, which is described in detail. In the nematic phase, the odd dimers are found to exhibit rather low order parameters with 〈P₂〉 taking values between 0.3 and 0.5 and 〈P₄〉 about 0.25. In contrast, the even dimer shows extremely high values of the order parameters with 〈P₂〉 taking values between 0.7 and 0.8 and 〈P₄〉 between 0.4 and 0.45. For the odd dimers, the values of 〈P₂〉 in the N_TB phase are similar to those of the N phase, whereas 〈P₄〉 jumps by approximately 5–10% and then decreases with temperature. On comparing the experimental data with the theoretical predictions, we find reasonable qualitative agreement for all materials with molecular field theory. The odd dimers, however, show higher 〈P₄〉 values than obtained from theoretical models, a factor attributed to the neglect of molecular flexibility and biaxiality in the PRS analysis.