Moments of the probability density function of R₂ approached via conditional probabilities. III. Models containing correctly as well as incorrectly placed atoms in the space groups P1 and P

First and second moments of P(R₂) are evaluated for models containing correctly as well as incorrectly placed atoms, denoted symbolically by {g, f}. Formulas are derived, valid for the space groups P1 and P, using explicitly the set of observed reflections. Extrapolation through the introduction of an averaged structure allows some general conclusions to be drawn concerning possible strategies used in automated structure determinations. A select elimination of data points from the R₂ check on the correctness of an atomic position severely limits the usefulness of the R₂ criterion. A check based on Rⁿ₂ has no better characteristics than one based on R₂. An R₂ criterion together with a zero-atom strategy has better chances of being successful than a random-atom approach.