An alternative to Hamilton's R-factor ratio test with special application to atom-assignment problems in crystallography

A procedure is given for estimating the variance ratio σ²₁/σ²₁₁, of two models of a crystal structure where σ²₁ and σ²₁₁ are the variances of the weighted (|F_o| - |F_c|) distributions for models I and II, respectively, and |F_o| and |F_c| are the observed and calculated structure factors. The procedure provides a statistical test of the hypothesis that the above ratio is unity for a given pair of models and, thus, whether one of the models offers a significantly better description of the crystal structure. The method is applicable to crystallographic problems in which each of two or more structural models is expressed in terms of the same set of parameters. It has been applied to a number of atom-assignment problems, and the results are compared with those from Hamilton's R-factor ratio test.