Random and systematic errors

Simon Parsons and William Clegg

in Crystal Structure Analysis

Second edition

Published in print June 2009 | ISBN: 9780199219469
Published online September 2009 | e-ISBN: 9780191722516 | DOI:

Series: International Union of Crystallography Texts on Crystallography

Random and systematic errors

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This chapter outlines some basic statistical methods and shows their application in crystallography, particularly in analysing the results. Concepts include: random and systematic errors, precision and accuracy, and distributions and their properties. Important properties include the mean and standard deviation of a distribution. The normal (Gaussian) distribution is of particular importance in view of the Central Limit Theorem. The mean of a set of values may be weighted or unweighted, and the place of weights in crystallography is discussed, especially in structure refinement. Some statistical tests and tools are described and used, including normal probability plots and analyses of variance. Correlation and covariance among parameters and derived results are considered. Possible sources of systematic and other errors in crystal structures are listed and their impact assessed. A simple checklist is provided for assessing results.

Keywords: statistics; random errors; systematic errors; precision and accuracy; distributions; weights; statistical testing; normal probability plot; analysis of variance; correlation and covariance

Chapter.  11608 words.  Illustrated.

Subjects: Crystallography

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