International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C, ch. 8.5, p. 707

## Section 8.5.1. Accuracy

E. Princea and C. H. Spiegelmanb

aNIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA, and bDepartment of Statistics, Texas A&M University, College Station, TX 77843, USA

### 8.5.1. Accuracy

| top | pdf |

Chapter 8.4 discusses statistical tests for goodness of fit between experimental observations and the predictions of a model with adjustable parameters whose values have been estimated by least squares or some similar procedure. In addition to the estimates of parameter values, one can also make estimates of the uncertainties in those values, estimates that are usually expressed in terms of an estimated standard deviation or, according to recommended usage (ISO, 1993), a standard uncertainty. A standard deviation is a measure of precision, that is, a measure of the width of a confidence interval that results from random fluctuations in the measurement process. What the experimenter who collected the data wants to know about, of course, is accuracy, a measure of the location of a region within which nature's `correct' value lies, as well as its width (Prince, 1994). In performing a refinement, we have assumed implicitly that the observations have been drawn at random from a population the mean of whose p.d.f. is given by a model when all of its parameters have those unknown, correct values. If this assumption is incorrect, the expected value of the estimate may no longer be near to the correct value, and the estimate contains bias, or systematic error. An accurate measurement is one that not only is precise but also has small bias. In this chapter, we shall discuss various criteria by which the results of a refinement may be judged in order to determine whether they are free of systematic error, and thus whether they may be considered accurate.

### References

ISO (1993). Guide to the expression of uncertainty in measurement. Geneva: International Organization for Standardization.
Prince, E. (1994). Mathematical techniques in crystallography and materials science, 2nd ed. Berlin/Heidelberg/New York/London/Paris/Tokyo/Hong Kong/Barcelona/Budapest: Springer-Verlag.