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Published online by Cambridge University Press: 05 June 2012
… [When] you can measure what you are speaking about and express it in numbers, you know something about it; but 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, whatever the matter may be.
Lord KelvinIn science, it's not enough to perform a measurement or make an estimate and report a number. It is equally important that you quantify how well you know the number. This is crucial for comparing measurements, testing theories, debunking bad models, and making real-world decisions. In order to do this, you need to know something about basic measurement theory, and how different sources of uncertainty combine to influence your final results. In this chapter we will be going over the fundamental statistical concepts that lie underneath all that we do when analyzing our data and models. We discuss some important issues that lie at the heart of measurement theory (scales, errors, and roundoff) and look at the concept of probability distributions. Related to this is the very delicate question of whether, how, and why some experimental data should be rejected. In short, this chapter summarizes the science of knowing what you know and how well you know it.
Measurement theory
Systems of measurements (scales)
How we measure or characterize things in science depends on our objectives.
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