Admissible Scale Transformation

As seen, for each scale of measurement, Stevens identified a class of admissible transformations, i.e., a function Φ that, when applied to the scale of interest produces another acceptable scale. For instance, in the case of height, any acceptable scale can be transformed into another acceptable scale through the product by a positive constant: Φ(x) = a⋅x, being a > 0 (cf. Table 3.1). Thus, we transform from inches to meters by multiplying by 0.0254 and from inches to feet by multiplying by 1/12. Multiplication by a positive constant defines an admissible transformation. All admissible transformations can be described this way.

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