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.