J. Ihringer, A QUANTITATIVE MEASURE FOR THE GOODNESS-OF-FIT IN PROFILE REFINEMENTSWITH MORE THAN 20 DEGREES OF FREEDOM, Journal of applied crystallography, 28, 1995, pp. 618-619
A quality indicator N-sigma is defined that exhibits immediately the s
ignificance level of the result of a least-squares refinement. For a r
efinement with nu degrees of freedom, N-sigma = (M- nu)/(2 nu)(1/2) ex
presses 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 a
ny nu > 20, \N-sigma\ should be as small as possible; however, it shou
ld be <3 for a sufficiently good refinement. Thus, N-sigma is a quanti
tative measure for the conformity of data, their weights and the model
, independent of the number of the degrees of freedom nu.