Abstract
STEVENS's1 classification of types of scaling according to their group structure appears insufficient, since a higher ordered metric2,3 and an interval scaling both belong to the same group, namely, the linear group (an interval scaling according to Stevens and a higher ordered metric scaling because the only function ƒ(x) such that for all a, b, c, d, if ∣a−b∣ > ∣c−d∣ then ∣ƒ(a)−ƒ(b)∣ > ∣ƒ(c)−ƒ(d)∣ is a linear function), yet they contain different amounts of information.
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References
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Shapiro, M. B., Brit. J. Med. Psychol., 34, 151 (1961).
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PHILLIPS, J. Scaling and Personal Questionnaires. Nature 200, 1347–1348 (1963). https://doi.org/10.1038/2001347b0
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DOI: https://doi.org/10.1038/2001347b0
