International
Tables for Crystallography Volume F Crystallography of biological macromolecules Edited by M. G. Rossmann and E. Arnold © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. F. ch. 18.5, p. 403
Section 18.5.1.2. Accuracy and precision^{a}Chemistry Department, UMIST, Manchester M60 1QD, England |
A distinction should be made between the terms accuracy and precision. A single measurement of the magnitude of a quantity differs by error from its unknown true value λ. In statistical theory (Cruickshank, 1959), the fundamental supposition made about errors is that, for a given experimental procedure, the possible results of an experiment define the probability density function f(x) of a random variable. Both the true value λ and the probability density f(x) are unknown. The problem of assessing the accuracy of a measurement is thus the double problem of estimating f(x) and of assuming a relation between f(x) and λ.
Precision relates to the function f(x) and its spread.
The problem of what relationship to assume between f(x) and the true value λ is more subtle, involving particularly the question of systematic errors. The usual procedure, after correcting for known systematic errors, is to suppose that some typical property of f(x), often the mean, is the value of λ. No repetition of the same experiment will ever reveal the systematic errors, so statistical estimates of precision take into account only random errors. Empirically, systematic errors can be detected only by remeasuring the quantity with a different technique.
Care is needed in reading older papers. The word accuracy was sometimes intended to cover both random and systematic errors, or it may cover only random errors in the above sense of precision (known systematic errors having been corrected).
In recent years, the well established term estimated standard deviation (e.s.d.) has been replaced by the term standard uncertainty (s.u.). (See Section 18.5.2.3 on statistical descriptors.)
References
Cruickshank, D. W. J. (1959). Statistics. In International tables for X-ray crystallography, Vol. 2, edited by J. S. Kasper & K. Lonsdale, pp. 84–98. Birmingham: Kynoch Press.Google Scholar