### Acta Crystallographica Section A

# Foundations of Crystallography

### Volume 69, Part 6 (November 2013)

## research papers

### 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, <^{2}>, <*I*_{o}^{2}>, <*I*_{o}^{2}/^{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.

**Keywords: theoretical residual values; data-quality indicators; fit-quality indicators; quality indicators.**

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