A QUANTITATIVE MEASURE FOR THE GOODNESS-OF-FIT IN PROFILE REFINEMENTS WITH MORE THAN 20 DEGREES OF FREEDOM

A quality indicator N-sigma is defined that exhibits immediately the significance level of the result of a least-squares refinement. For a refinement with nu degrees of freedom, N-sigma = (M- nu)/(2 nu)(1/2) expresses the deviation of the deviance M from its expected value nu in terms of its standard deviation (2 nu)(1/2) The deviance M is the sum of weighted squared differences between observed and model data. For any nu > 20, \N-sigma\ should be as small as possible; however, it should be <3 for a sufficiently good refinement. Thus, N-sigma is a quantitative measure for the conformity of data, their weights and the model, independent of the number of the degrees of freedom nu.