Empirical Test of Scale Type Resulting from the Power Law for Heaviness

Abstract

Stevens claims the ratio-scale level for the scale values resulting from direct scaling procedures and the Power Law, whereas according to Torgerson only a logarithmic transformation of these values leads to an interval scale. Both hypotheses are evaluated for the continuum of heaviness by testing empirically an axiom of a Finite, Equally-spaced Difference Structure, with the Neyman-Pearson test of significance as an error theory. The reported subjective differences in heaviness are represented by numerical differences between scale values resulting from the Power Law but not by differences between logarithmic transformed scale values. Subjective ratios, on the other hand, are not represented by ratios between the values resulting from the Power Law. The Power Law for heaviness leads to an interval scale, not to a ratio scale.