Читать книгу Applied Univariate, Bivariate, and Multivariate Statistics - Daniel J. Denis - Страница 39

Measurement at the interval level possesses all the features of measurement of both nominal and ordinal scales, but with the extra requirement that distances between measured objects are quantifiable, and that distances between successive measuring points on the scale are equal in magnitude. For instance, consider the measurement of temperature in degrees Fahrenheit. The change in temperature from 10 degrees to 20 degrees essentially contains the same “amount” of temperature change as that from 20 to 30 degrees. That is, the intervals between measurement points are meaningful and represent an equal distance in the “thing” (i.e., temperature, in this case) we are measuring.

Is intelligence measurable on an interval scale? What would it mean for it to be measurable at the interval level? Well, supposing we base our measurements on a reputable standardized test, for IQ to be measurable at the interval scale would imply that the distance in the thing called “IQ” is equivalent from say, 90 to 100 as it is from 100 to 110. At first glance, this might appear an easy condition to satisfy, after all, the real number distance in each interval is equal to 10. However, recall that that is a distance of real numbers, not necessarily of IQ. As William James put it, we must not confuse the phenomena we study with the abstractions we use to study them. The real numbers are the abstraction. The IQ is the phenomenon. That we used a real line to measure these distances does not necessarily imply that the actual true distances in terms of “IQ substance” corresponds one‐to‐one (or even at all) to our measurement tool. It is entirely possible that 90 to 100 represents a greater increase in IQ than does 100 to 110, making the relation between our measurement of IQ versus “true IQ,” nonlinear. Our measurement of IQ is simply not that precise to make such statements. Numerical length in this case may not translate to the substantive length of the difference under study.