Moments of the probability density function of R₂ approached via conditional probabilities. IV. Influence of the elimination of (low-intensity) data on the applicability of R₂ in automated structure evaluation

The average value of the residual R₂ and its spread σ(R₂) is described as a function of a threshold a, below which E_o² values are omitted from the data set. Theoretical expressions, valid for finite data sets in the space groups P1 and P, are derived for (R₂) and σ(R₂) as functions of a for models containing atoms correctly as well as incorrectly positioned. Use of a threshold causes a decrease in the resolving power of R₂-based strategies used in automated structure evaluations. Random elimination of E_o values gives rise to a larger loss of resolving power than does the elimination of small E_o values.