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The bootstrap statistical method is applied to the analysis of single-crystal X-ray diffraction data of tazheranite [(Zr,Ca,Ti)O 2 ; cubic,  a  = 5.117 Å], in order to establish the significance of statistical estimators of noncentrosymmetricity. The lack of the inversion centre is successfully proved showing that the average structure of tazheranite has space group  F [unk]3 m , due to a different repartition of oxygen vacancies between two sites of the fluorite-type structure. Instead, classical estimators of the intensity distribution and of the refinements were not able to discriminate between  Fm [unk] m  and  F [unk]3 m  space groups.

The bootstrap method as a test for non-centrosymmetricity – Application to tazheranite (Zr,Ca,Ti)O 2