Measurement

Historical Perspectives on Measurement

For some, measurement is simply a tool of statistics, a necessary predecessor. We cannot perform statistical analyses if we have not measured anything. Consequently, some would say that measurement is simply the handmaiden of statistics. They might be inclined to take the point of view of S. S. Stevens, who defined measurement as “the assignment of numerals to objects or events according to a rule.” Stevens went on to propose four scales of measurement: nominal, ordinal, interval, and ratio.

Nominal scales are made up of variables with levels that are qualitatively different from one another. For example, consider the variable “ethnic background.” This variable could consist of any number of levels, but for the purposes of this example, let us consider just a few possibilities. A participant might report being Asian, African American, Latino, or Native American. Each of these different levels of the ethnic background variable represents a qualitatively different category. More specifically, each category is mutually exclusive of the others.

A second scale of measurement is an ordinal scale. Within the context of ordinal scales, the researcher is typically interested in knowing something about the rank order of the levels of the variable; however, there is no implication that these levels differ by any fixed amount. Perhaps the classic example of ordinal-level measurement is found in the Olympic Games, where athletes receiving medals are ranked from 1st to 3rd place. It does not matter whether the gold medalist beat the silver medalist to the finish line by a fraction of a second or by 10 minutes. What matters is the order in which the athletes reached the finish line. The first one to cross the finish line receives a ranking of 1, and the second one across receives a ranking of 2. The assumption within an ordinal scale of measurement is that the fundamental quantity of interest is the relative placement and not the absolute difference between points on the scale. Another practical example of an ordinal scale of measurement would be the percentile ranking a student receives on an examination.

A third scale of measurement proposed by Stevens is the interval scale. Interval scales of measurement have several useful properties. For example, the difference between any two points on the scale is always the same. This is not always true within the context of an ordinal scale (e.g., percentile rankings). It is important to note, however, that interval scales do not have a true zero point—that is, a zero does not necessarily imply the complete absence of the construct of interest. Consider, for example, the measurement of intelligence. A person may receive a score of zero on a particular intelligence test if he or she answered all items incorrectly. Even if a person were to answer incorrectly every item on the test and receive a score of zero, this does not imply that the person has absolutely no intelligence. His or her intelligence was simply not captured by the items on that particular test (e.g., consider a Western intelligence test that is administered to participants from a very different culture).

...