# Get e-book Foundations of Measurement. Representation, Axiomatization, and Invariance

Most of these psychological tests use so called Likert scales see this Wikipedia article. For example:. Given their widespread use, the question how useful such tests are has arisen many times; see here , here , or here. For example, Carifio and Perla assume that underlying each response format ranging from e.

### 2. Uniqueness of the Representation

Thus, they hold the philosophical view that each psychological attribute must be metric. They do not present any grounds for that stark claim. Similarly, they assume that each of such scales maps an empirical quantitative attribute. And they assume without any consideration that some given items they call it a scale , automatically measure the same underlying quantity if existing.

Besides their stark language, I am strongly disagree with many points they are rising. Sadly, they fail to mention even the most basic aspects of measurement theory see here for a nice introduction; read the work of Michell for a more in-depth reasoning.

## Why Likert scales are (in general) not metric – Sebastian Sauer Stats Blog

For example, one proponent that Likert scales generally do exhibit interval metric level is is Labovitz, eg. However, other scholars have insisted that Likert scales do not generally possess metric level, and that demonstrating metric niveau is quite a delicate job. Maybe the most pronounced critic is Joel Michell, see e. Krantz, D. Suppes, P.

Luce, R. What is meant by equidistance? It means that, for example, the difference in weight between 1 kg and 2 kg should be equal to the difference in weight between 2 kg and 2 kg.

I think, the short answer is: We cannot take it for granted that the distances are equal; why should they? If we are ignorant or neutral, it appears for more likely that the distances are not equal, as it appears more likely that any two number are different rather than equal.

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Suppose 10 sprinters are running the meters, with different times:. Some say sorry, did not find a citation, but one of my teachers said so!

I cannot see why this must necessarily happen. Suppose we would not have 10 but sprinters; the picture and the argument would in essence remain the same. Equidistance will not necessarily pop out. It may by chance occur, but it is not a necessity by far not. Now, if we were to have many items, can we then infer that equidistance will necessarily come out? Assume that the measurement error is negligible to make things easier but without loss of generality.

If measurement error is negligible, then the actual performance, ie. Campbell, N. The Elements. Cambridge: Cambridge University Press.

## Foundations of Measurement Volume III: Representation, Axiomatization, and Invariance

Google Scholar. Cohen, M. Fundamental unit structures: A ratio scalability. Coombs, C.

### Análisis Matemático

Mathematical Psychology. Englewood Cliffs, NJ: Prentice. Droste, M. Ordinal scales in the theory of measurement. Ellis, B. Basic Concepts of Measurements. Khurshid, A. Scales of measurements: An introduction and a selected bibliography. Krantz, D. Suppes, P.

New York: Academic Press. Lissitz, R. Reporting NAEP results using standards. Educational Measurement: Issues and Practice 14 2 : 14— Luce, R. Dimensionally invariant numerical laws correspond to meaningful qualitative relations. Philosophy of Science 1— San Diego: Academic Press. Classification of concatenation measurement structures according to scale type.

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Narens, L. A general theory of ratio scalability with remarks about the measurement theoretic concept of meaningfulness. Theory and Decision 1— Measurement: The theory of numerical assignments. Psychological Bulletin 99 2 : — Pfanzagl, J. Theory of Measurement.