This article describes eight studies that tested empirically
the hypothesis that rating procedures lead to
interval-scale measurements for each single subject. In
order to enhance the probability of obtaining interval
scales, subjects made numerical ratings and were deliberately
instructed to choose their responses so that
the algebraic differences between numbers represented
the subjective differences between the corresponding
objects with respect to the attribute under study. This
approach is based on axiomatic measurement theory.
It is exemplified by a study from clinical psychological
research pertaining to the subjective fear aroused
by each of 160 objects or situations. Any subject’s
ratings are regarded as interval-scale measurements of
his or her individual degree of fear if the testable axioms
of a finite, equally-spaced difference structure
are satisfied empirically. These axioms pertain to ordinal
judgments on differences, and they are tested empirically
by deriving statistical hypotheses and using a
refined significance-test method as an error theory.
For the eight studies criteria were chosen primarily to
avoid accepting false interval-scale hypotheses at the
expense of relative high risks for false rejections.
Nevertheless, empirical data allow acceptance of the
hypothesis for 54 of the 114 subjects. As a consequence,
for at least half of the subjects, this rating
procedure seems to result in interval scales.