Foremost among the ratio scales is the scale of number itself-cardinal number-the scale we use when we count such things as eggs, pennies, and apples. This scale of the numerosity of aggregates is so basic and so common that it is ordinarily not even mentioned in discussions of measurement.
Note on absolute scales The so-called absolute scale is a special ratio scale which is used whenever counting items. Apart from a non-arbitrary zero, this scale also includes a non-arbitrary unit, corresponding to the single item. The application of transformations Φ(x) = a⋅x (being a > 0) to absolute scales—although being admissible for ratio scales in general—would “distort” the unit, leading to the loss of its physical meaning. In this case, the only admissible scale transformation would be the “identity” Φ(x) = x (Roberts 1979).
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