To calculate aerosol extinction from Raman lidar data, it is necessary to evaluate the derivative of a molecular Raman signal with respect to range. The typical approach taken in the lidar community is to make an a priori assumption about the functional behavior of the data to calculate the derivative. It has previously been shown that the use of the chi-squared technique to determine the most likely functional behavior of the data prior to actually calculating the derivative eliminates the need for making a priori assumptions. Here that technique is validated through numerical simulation and by application to a significant body of Raman lidar measurements. In general, we show that the chi-squared approach for evaluating extinction yields lower extinction uncertainty than traditional techniques. We also use the technique to study the feasibility of developing a general characterization of the extinction uncertainty that could permit the uncertainty in Raman lidar aerosol extinction measurements to be estimated accurately without the need of the chi-squared technique.