On the Role of Statistical Weighting in the Least-Squares Analysis of UV-Visible Spectrophotometric Data

Abstract

Spectrophotometric data are inherently heteroscedastic, which means that least-squares component analyses of absorbance spectra should properly employ weighted fits. The effects of neglecting weights (the common practice) is examined through Monte Carlo calculations on a three-peak model having two closely overlapping components of comparable strength and a third component that appears as a weak shoulder. The results show statistically significant loss of precision in all parameters; however the magnitude of this loss is ≤30% for realistic conditions. For comparison, experimental spectra of I2 in CCl4 (which was the basis for the Monte Carlo test model) are similarly analyzed. These results suggest that model inadequacy is likely to be a greater practical problem than neglect of weights, because the great precision of spectrophotometric data places extreme demands on the fit model. In the present instance, for example, incorporation of a correction term for the sinusoidal error in the spectrometer wavelength significantly reduces the fit chi-square.