Since its inception more than 60 years ago, a “reliability index”, later called “R-value”, has been used to measure the agreement of model and averaged data, and a similar quantity, Rmerge, has been defined to assess the quality of the averaged data.
However, a little known fact is that the two kinds of R-values have very different properties and asymptotic behaviors, and cannot be compared with ... [Show full abstract] each other. This is the reason that decisions concerning the high-resolution cutoff of data that are based on these R-values are questionable, and also helps explain why disagreements between journal authors and the manuscript reviewers have been so common.
Here, the authors will show that a different statistic can be used to overcome these deficiencies, and will establish a direct quantitative relation between data and model quality. This relation is important to judge the extent to which the data are useful, and also gives insight into the quality of the model that is derived from the data. The theoretical and practical consequences are at variance with several commonly employed crystallographic concepts and procedures.