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 theoreticalRvalues 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 ofRvalues as presented here is applicable to any field where model parameters are fitted to data with known precision. For crystallographic applications,F2-based residual benchmark values are given. They depend on the first and second moments of variance, intensity and significance distributions, 〈σ2〉, 〈Io2〉, 〈Io2/σ2〉. Possible applications of the theoreticalRvalues are, for example, as a data-quality measure or the detection of systematic deviations between experimental data and model predicted data, although the theoreticalRvalues cannot identify the origin of these systematic deviations. The change inRvalues due to application of a weighting scheme is quantified with the theoreticalRvalues.