An Introduction to Uncertainty in Measurement Book contents
- Frontmatter
- Contents
- Dedication
- Preface
- 1 The importance of uncertainty in science and technology
- 2 Measurement fundamentals
- 3 Terms used in measurement
- 4 Introduction to uncertainty in measurement
- 5 Some statistical concepts
- 6 Systematic errors
- 7 Calculation of uncertainties
- 8 Probability density, the Gaussian distribution and central limit theorem
- 9 Sampling a Gaussian distribution
- 10 The t-distribution and Welch–Satterthwaite formula
- 11 Case studies in measurement uncertainty
- Appendix A Solutions to exercises
- Appendix B 95% Coverage factors, k as a function of the number of degrees of freedom, v
- Appendix C Further discussion following from the Welch–Satterthwaite formula
- References
- Index
2 - Measurement fundamentals
Published online by Cambridge University Press: 06 July 2010
- Frontmatter
- Contents
- Dedication
- Preface
- 1 The importance of uncertainty in science and technology
- 2 Measurement fundamentals
- 3 Terms used in measurement
- 4 Introduction to uncertainty in measurement
- 5 Some statistical concepts
- 6 Systematic errors
- 7 Calculation of uncertainties
- 8 Probability density, the Gaussian distribution and central limit theorem
- 9 Sampling a Gaussian distribution
- 10 The t-distribution and Welch–Satterthwaite formula
- 11 Case studies in measurement uncertainty
- Appendix A Solutions to exercises
- Appendix B 95% Coverage factors, k as a function of the number of degrees of freedom, v
- Appendix C Further discussion following from the Welch–Satterthwaite formula
- References
- Index
Summary
Lord Kelvin, a renowned scientist born in Ireland in the nineteenth century, recognised the importance of measurement and spoke about it in passionate terms:
When you can measure what you are speaking about and express it in a number, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the state of science …
(Lecture given to the Institution of Civil Engineers, 3 May 1883)Measurement is essential to science. Without measurement, scientific models and theories cannot be rigorously tested or challenged. Ambitious scientific and technical endeavours such as the exploration of the surface of Mars, medical diagnosis using magnetic-resonance imaging (MRI) and the evaluation of renewable energy sources would not be possible. Measurement is no less critical in areas such as international trade, with the global economy becoming ever more pervasive.
In this chapter we consider matters key to measurement and the communication of the results of measurement. These include the system of units, scientific notation and significant figures.
The system of units of measurement
To measure the length of a particular object and have the result of that measurement recognised and understood by other people, there must be mutual agreement on a basic unit of length. Over past centuries many units have been adopted as the basis of length measurement in different parts of the world. Some of those units, like the metre, the mile and the fathom, are still in use today.
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- An Introduction to Uncertainty in MeasurementUsing the GUM (Guide to the Expression of Uncertainty in Measurement), pp. 15 - 26Publisher: Cambridge University PressPrint publication year: 2006
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