title: More about residual values.
abstract: The usual residual values are complemented by expectation values based solely on the experimental data and the number of model parameters. These theoretical R values serve as benchmark values when all of the basic assumptions for a least-squares refinement, i.e. no systematic errors and a fully adequate model capable of describing the data, are fulfilled. The prediction of R values as presented here is applicable to any field where model parameters are fitted to data with known precision. For crystallographic applications, F(2)-based residual benchmark values are given. They depend on the first and second moments of variance, intensity and significance distributions, <σ(2)>, <Io(2)>, <Io(2)/σ(2)>. Possible applications of the theoretical R values are, for example, as a data-quality measure or the detection of systematic deviations between experimental data and model predicted data, although the theoretical R values cannot identify the origin of these systematic deviations. The change in R values due to application of a weighting scheme is quantified with the theoretical R values.
authors.affiliation: Laboratory of Crystallography, University of Bayreuth, 95440 Bayreuth, Germany.
authors.forename: Julian
authors.initials: J
authors.lastname: Henn
authors.forename: Andreas
authors.initials: A
authors.lastname: Schönleber
keywords: data-quality indicators; fit-quality indicators; quality indicators; theoretical residual values