Applied psychological measurement scales for the most part are nominal- or ordinal-level scales, although many scales and tests commonly used approximate interval measurement well enough for practical purposes. Strictly speaking, intelligence, aptitude, personality, and performance scales are ordinal-level measures. They indicate not the amounts of intelligence, aptitude, personality traits, or performance of individuals, but rather their rank order with respect to the constructs in question. Yet, with a considerable degree of confidence, we can often assume an equal interval scale, as Kerlinger and Lee (2000) noted: Though most psychological scales are basically ordinal, we can with considerable assurance often assume equality of interval. The argument is evidential. If we have, say, two or three measures of the same variable, and these measures are all substantially and linearly related, then equal intervals can be assumed. This assumption is valid because the more nearly a relation approaches linearity, the more nearly equal are the intervals of the scales. This also applies, at least to some extent, to certain psychological measures like intelligence, achievement, and aptitude tests and scales. A related argument is that many of the methods of analysis we use work quite well with most psychological scales. That is, the results we get from using scales and assuming equal intervals are quite satisfactory. (p. 637).
The argument is a pragmatic one that has been presented elsewhere (Ghiselli et al., 1981). In short, we assume an equal interval scale because this assumption works.