Statistical tests against systematic errors in data sets based on the equality of residual means and variances from control samples: theory and applications

Acta Crystallographica. Section A, Foundations and Advances
Julian Henn, Kathrin Meindl

Abstract

Statistical tests are applied for the detection of systematic errors in data sets from least-squares refinements or other residual-based reconstruction processes. Samples of the residuals of the data are tested against the hypothesis that they belong to the same distribution. For this it is necessary that they show the same mean values and variances within the limits given by statistical fluctuations. When the samples differ significantly from each other, they are not from the same distribution within the limits set by the significance level. Therefore they cannot originate from a single Gaussian function in this case. It is shown that a significance cutoff results in exactly this case. Significance cutoffs are still frequently used in charge-density studies. The tests are applied to artificial data with and without systematic errors and to experimental data from the literature.

References

Apr 19, 2008·Acta Crystallographica. Section A, Foundations of Crystallography·Kathrin Meindl, Julian Henn
Apr 21, 2010·Acta Crystallographica. Section A, Foundations of Crystallography·Kathrin MeindlJulian Henn
Oct 22, 2010·Acta Crystallographica. Section A, Foundations of Crystallography·Julian Henn, Kathrin Meindl
Feb 18, 2011·Acta Crystallographica. Section A, Foundations of Crystallography·Vladimir V ZhurovA Alan Pinkerton
Jul 22, 2011·Acta Crystallographica. Section B, Structural Science·Agnieszka PaulClaude Lecomte
Dec 18, 2012·The Journal of Physical Chemistry. a·Regine Herbst-IrmerDietmar Stalke
Oct 18, 2013·Acta Crystallographica. Section A, Foundations of Crystallography·Julian Henn, Andreas Schönleber
May 13, 2014·Acta Crystallographica. Section A, Foundations and Advances·Julian Henn, Kathrin Meindl
Sep 2, 2014·Acta Crystallographica. Section A, Foundations and Advances·Julian Henn, Kathrin Meindl
Oct 3, 2014·Acta Crystallographica Section B, Structural Science, Crystal Engineering and Materials·Katarzyna N JarzembskaMichał K Cyrański

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Citations

Feb 27, 2016·Acta Crystallographica. Section A, Foundations and Advances·Bertrand FournierPhilip Coppens
Nov 4, 2016·Acta Crystallographica. Section A, Foundations and Advances·Julian Henn
Aug 2, 2017·Acta Crystallographica Section B, Structural Science, Crystal Engineering and Materials·Regine Herbst-Irmer, Dietmar Stalke
Jul 21, 2020·Journal of Applied Crystallography·Lennard KrauseJacob Overgaard
Apr 1, 2019·Acta Crystallographica Section B, Structural Science, Crystal Engineering and Materials·Vladimir G TsirelsonIlya V Tokatly

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