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Quality & Quantity

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15.07.2016

Measurement in social research: some misunderstandings

verfasst von: Alessandro Bruschi

Erschienen in: Quality & Quantity | Ausgabe 5/2017

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Abstract

The concept of numerical measurement based on the manipulation of objects has impoverished and distorted the meaning of magnitude and scale. This article aims to contribute to a concept of the most fruitful measurement for the development of the social sciences, with reference to specific aspects indicating the differences from the natural one and regarding, in particular, the non-numeric.

Vorheriger Artikel Structure of the labour market and wage inequality: evidence from European countries

Nächster Artikel Gender discrimination in education, health, and labour market: a voice for equality

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According to Stevens “The numerosity of collections of objects (number in the layman sense) constitutes the oldest and one of the most basic scales of measurement. It belongs to the class that I have called ratio scales” (1959, p. 20). But, in this interpretation, ratio scales become both those that give rise to a discrete, natural, and to a continuous, real numerical measurement.

The general validity of the division of physical properties into extensive and intensive kinds, introduced by Tolman, has been addressed in the course of science. Redlich noted that these two categories are not inclusive of all the properties (1970).

The distinction recalls that of extensive and intensive classification, but the two classifications are based on different criteria: the extensive/intensive on intrinsic properties of magnitudes, the other on operations that are performed for the measurement. And in fact the distinction between extensive properties and intensive does not coincide with that between fundamental and derived of Campbell. There are properties such as temperature which, despite being considered fundamental, are intensive.

This is the Ellis classification with some differences. For Ellis there are at least four types of measurement: elementary, fundamental, associative, and derived (1966, pp. 58–67). The first two are direct, distinct in fundamental and elementary, where elementary is the ordinal scale, common to all quantitative magnitudes, because, if a quantity exists, it has a relation of order; fundamental is one direct that allows additive operations. The associative and the derivatives are indirect. I deleted the elementary because it does not concern the priority, but the level of measurement.

According to the IS, fundamental are those fundamental of Campbell and the associative ones; all other are derived.

In Book V of the Metaphysics, par. 13, Aristotle says that "one thing has quantity when it is divisible into parts that belong to it, and each part is by nature something of a single particularly determined one. A quantity is a multiplicity if is countable, a magnitude if it is measurable. It is said multiplicity which is potentially divisible in parts that are not continuous; it is said magnitude which is divisible into continuous parts." (2014, p. 321).

Actually Campbell (1957, p. 327) does not exclude other ways of doing numerical assignments but, in his opinion, it is hard to discuss their possibility, not finding examples in physics.

As well as, with some differentiation, in the work of Pfanzagl (1968) and Narens (1981). For an analysis of the development of the RT, see Martin (2003).

However, it was observed that the Rasch model is based on a probabilistic logic, while that of the SCM is deterministic. It also leaves doubtful the relationship between the empirical and the formal structures of the IRT, which is denied by Kyngdon (2008), because he considers the first ones as formal and numerical as the second ones, produced by parameter estimates and probability. Michell (2008) believes that the logic of Rasch model differs from that of SCM, it does not reach the final result by controlling the order relations of joint propriety, but using a function between property intensity and response probability.

But later Stevens seems to have some doubt, stating: “Although the definition of measurement could, if we wished, be broadened to include the determination of any kind of relation between properties of objects or events, it seems reasonable, for the present, to restrict its meaning to those relations for which one or another propriety of the real number system might serve as a useful model” (Stevens 1959, p. 24).

Moreover, subjects can be compared even if the same items are not administered to them. Further advantages come from the greater precision of the IRT tools in measuring specific levels of a property, for which tests with a few items may have a high level of information, unlike what happens in the classical measurement, where accuracy goes up increasing their number.

And Pap, in a more liberal way, considered magnitude a property measurable only in a numerical sense, when it is continuous or at least amenable to cardinal measurement (1962, chap. 8).

There is also the problem of the theoretical validity of the criterion used (the other scale) for the control, because both scales may not be valid, or not be just the one introduced as a criterion.

For a comparison between the two measurements, see also Finkelstein (2003, 2009).

For a history of the relations between sociology and mathematics see Capecchi (2010).

As is evidenced by the debate on Qualitative Comparative Analysis. We can refer to, among others, the contributions in Sociological Theory and Methods, in Studies in Comparative International Development, in Sociological Methodology, and the recent contribution by Lucas and Szatrowski (2014) with a vast bibliography to this regard.

So, for Torgerson numerical labels can be used to name the classes, but the fact that a librarian assigns the number 8105 to a book does not mean that he has measured the book; otherwise, the classification, and even the name of the individual cases become a form of measurement (Torgerson 1958: pp. 9, 14). And, according to Sartori, a nominal scale is only a classification, not a scale that measures something; certainly, also the items of a classification may be numbered: but this is just a coding gimmick that has nothing to do with a quantification (Sartori 1971, p. 53).

According to McDonald the question is not whether the scale fulfills the properties of a given level of measurement, but if the statistical required assumptions are fulfilled and the statistical hypotheses remain invariant to the change of scale (1999, p. 418). See also Labovitz (1970, p. 515), Velleman and Wilkinson (1993).

See Acock and Martin (1974), Grether (1979), Young (1981), Henry (1982), O'Brien (1985).

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Titel: Measurement in social research: some misunderstandings
verfasst von: Alessandro Bruschi
Publikationsdatum: 15.07.2016
Verlag: Springer Netherlands
Erschienen in: Quality & Quantity / Ausgabe 5/2017
Print ISSN: 0033-5177
Elektronische ISSN: 1573-7845
DOI: https://doi.org/10.1007/s11135-016-0383-5

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