We describe the order parameter S(T) of liquid crystals in the nematic state by a four-parameter expression which is consistent with mean-field theory. A two-step fitting method is applied to high resolution refractive index data for the nCB (n = 5 - 8) liquid crystals, processed according to Vuks and Neugebauer models. We find quasi-universal parameter values. The average critical exponent is beta = 0.241 +/- 0.012, in agreement with the mean-field prediction for a tricritical point. Thus the temperature dependence of the nematic order parameter is quasi-tricritical in all cases. The order parameter at the effective transition point T** is S** = 0.143 +/- 0.05 and the relative polarizability anisotropy Deltaalpha/[alpha] = 0.69 +/- 0.03. We show that earlier results using the Haller approximation were too low (beta = 0.16 - 0.19) because of the assumption S**= 0 and T**= T-NI. The chosen fitting function provides the best description of S( T) both close and far from T**. For all parameters, the alternating odd even effect with the number of C atoms in the alkyl chain is about +/- 5% except for S** for which it is +/- 30%. 6CB is singled out by a somewhat different set of fitting parameters. 8CB shows a pretransitional smectic behaviour starting from 4 K above the smectic - nematic transition point.