Expressing Uncertainty in Measurement

Measurement plays a key role in science. Without values obtained through accurate measurement, we are unable to place scientific ideas on a solid, quantitative footing, or verify or refute predictions based on theoretical considerations. Only when accurate values are available are we able to compare values obtained in experiments that are carried out in different laboratories.

Quantities, such as energy, magnetic field and momentum are preferentially measured in units derived from the base units in the SI system. While the scientific world has largely adopted the SI system of units, permitting scientists to compare values obtained through experiment in laboratories around the world, until comparatively recently there was no international consensus regarding how uncertainties in values should be expressed. The International Organisation for Standardisation (ISO) began work around 1980 to remedy this situation.

In pursuit of a standard way in which uncertainties in measurement may be expressed, the ISO prepared and published a document in 1993 called "Guide to the Expression of Uncertainty in Measurement" (often abbreviated to the 'GUM'). The GUM is widely considered as the 'definitive document' regarding the expression of uncertainty. Other documents have been prepared by other national and international bodies such as the National Institute of Standards and Technology (NIST) and European Accreditation (EA). These documents are based on the principles and advice contained in the GUM.

The GUM considers uncertainties which may be placed in one of two categories. Uncertainties which are categorised as 'Type A' are those which are evaluated by statistical methods. 'Type B' uncertainties are those which are evaluated by methods other than statistical (such as those which may be established from an instrument manufacturer's specification, a calibration certificate, or tables in a data book).

The hope and expectation is that, over time, uncertainties in values obtained through experiment or observation in all fields of science and engineering will be expressed in a manner consistent with the GUM document. Many bodies world wide that are responsible for the maintenance of standards and the calibration of instruments have already adopted these methods.

In order to properly describe the methods recommended by the ISO organisation, we must discuss and consider such terms as:

• error
• standard uncertainty
• combined standard uncertainty
• coverage factor
• expanded uncertainty
• effective degrees of freedom

The PDF file offers a discussion on error and uncertainty and pays particular attention to the GUM approach to calculating, combining and expressing uncertainties.

 Downloadable PDF file

For an article dealing with the topic non-linear least squares, please click on the link below.

Principles and Applications of Non-Linear Least Squares.

My email address is Les.Kirkup@uts.edu.au

Les Kirkup May 2003