Comparison of the σ(I)/I and Least-Squares Methods for Integration of Bragg Reflections

It is shown that peak integration by the σ(I)/I method is equivalent to a least-squares method that uses a weight matrix W ≠ V_y⁻¹, where V_y is the variance-covariance matrix of the observations. By the Gauss–Markov theorem, this gives variances for the estimated parameters that are greater, but in practice only slightly greater, than those obtained from an ideally weighted least-squares method.