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Measurement Report and Presentation

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Quality Assured Measurement

Part of the book series: Springer Series in Measurement Science and Technology ((SSMST))

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Abstract

Any report and presentation of measurement results will include both the measured value and some estimate of the measurement uncertainty in the measured value. In this penultimate chapter, and prior to the final step of decision-making covered in Chap. 6, we consider how best to model measurement information throughout the measurement process—from entity stimulus, through instrument response to restitution of the measurement value. A general and broad formulation is sought of differences applicable in both the physical and social sciences.

Rossi (Measurement and probability – A probabilistic theory of measurement with applications, in Springer Series in Measurement Science and Technology, 2014) in another book in this series gives an account of a probabilistic theory of measurement. In this chapter, we build on Rossi’s approach when presenting measurement for both the physical and social sciences; extending the probabilistic theory for treating measurement error and uncertainty by using concepts of entropy and symmetry.

The concept of entropy can in fact be invoked analogously to describe ‘dissipation of useful information’—to paraphrase Carnot—at each of the three main stages in the measurement process—from (A) object, through (B) measurement to (C) response—not only to make a descriptive presentation (as in probability theory of measurement) but also in an explanatory and predictive way.

The entropy concept can also help when presenting measurement results at every level in the quantity calculus hierarchy (Table 3.1) from mere labels for nominal syntax, through semantic and pragmatic measures, to a full expression in terms of the nature of the quantity measured and effectiveness in changing conduct. This approach is particularly useful for prioritising (Sect. 5.2.1) among a plethora of potentially important factors (such as identified in a critical incidence process). This discussion will also prepare the ground for the final chapter of book, when decisions about product (in the widest sense) based on measurement need to be made.

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Notes

  1. 1.

    A single entity which changes its property values during a measurement is considered as different entities.

  2. 2.

    ‘Y’ in Wold et al. (2001) corresponds to ‘Z’ in our notation.

  3. 3.

    https://en.wikipedia.org/wiki/Irreducible_representation.

  4. 4.

    It is easier to maximise the log-likelihood (which has the same maximum as the likelihood) since it is a sum rather than a product of terms, as in the case of the Rasch model.

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    Leslie Pendrill

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Pendrill, L. (2019). Measurement Report and Presentation. In: Quality Assured Measurement. Springer Series in Measurement Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-030-28695-8_5

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