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Keywords:

  • probability density functions;
  • normalized structure factors;
  • statistical analysis;
  • computer programs

Statistical analysis of the normalized structure factor E is important during space-group determination. Several approaches to solve this problem have been described in the literature. In this paper, the most popular approach, the ideal asymptotic probability density function developed by Wilson, is compared with the more accurate exact probability density functions described by Shmueli and co-workers. Furthermore, a new computer program, CentroMK, for normalized structure factor analysis, is presented. The program is capable of plotting histograms of the normalized structure factors and exact probability density functions. Moreover, the program calculates five estimators helpful during the space-group determination: 〈|E|〉, 〈|E2 − 1|〉, %E > 2, %E < 0.25 and the discrepancy R function. The two approaches and the error rates of the five listed estimators are compared for nearly 30 600 crystal structures obtained from Acta Crystallographica Section E. It is shown that within a space group the means 〈|E|〉 and 〈|E2 − 1|〉 of real crystal structures show high variability. The comparison shows that decisions based on the exact probability density function are more accurate, the computing time is reasonable, and estimators 〈|E|〉, %E < 0.25 and R are the most accurate and should be preferred during space-group determination.