Testing the hypothesis `no remaining systematic error' in parameter determination

Beu, Musil & Whitney [Acta Cryst. (1962), 15, 1292-1301; Acta Cryst. (1963), 16, 1241-1242] proposed a maximum-likelihood method of estimating the lattice parameters of cubic, tetragonal and hexagonal crystals, and a method of testing the hypothesis that systematic errors had been satisfactorily accounted for. The use of maximum likelihood is unnecessary, and open to some objection. The argument is therefore rewritten in the more familiar least-squares form, and is generalized to cover the remaining crystal systems. Only if systematic errors are absent is it legitimate to estimate standard deviations of parameters from the differences of observed and calculated Bragg angles. With minor modifications the results are applicable to structural parameters also.