Absolute and other scales: question of validity.

Abstract

In an article entitled Evidence against 'absolute' scaling, Mellers (1983)describes art experimental result she regards as proof that the absolute scaling advocated by Zwislocki and Goodman (1980) is no more absolute than ratio scaling by magnitude estimation or category scaling. The result concerns similar biases produced in all three scales by manipulation of a stimulus context. She presented 11 25-mm squares containing various numbers of irregularly distributed black dots and asked her subjects to scale the apparent darkness of the squares. The latter were shown simultaneously in one of two patterns of darkness distribution. In one pattern, the stimuli were bunched at the low end of their range, and in the other, at the high end. Sinceinstructions considered by Mellers as identical to those of Zwislocki and Goodman failed to reduce the biases associated with the skewed stimulus distributions, they do not lead to an absolute scale, she concludes. It appears to me that Meller's experiment is based on a fundamental misunderstanding of the concept of absolute scale accepted by Zwislocki and Goodman, which is derived from Stevens's (e.g., 1951) classification of scales and is much less ambitious than Mellers's. Stevens's classification is mathematically formal and based on permissible transformations under which the scales remain invariant. The highest levelscale he considers is the ratio scale, which allows only one transformation-multiplication by a constant. In his first fundamental article on magnitude estimation, Stevens (1956) describes biases resulting from such a transformation, however, and shows that the scale biased the least according to his criteria is obtained when the experimental subjects (observers) are allowed to choose their own reference standards or moduli. This amounts to choosing their own units. As shown on several occasions (e.g., Hellman & Zwislocki, 1961; Zwislocki & Goodman, 1980), the choice is not arbitrary. If units of measurement cannot be designated arbitrarily by the experimenter, so that even a multiplicative transformation is excluded, the scale must become formally absolute.