1.3 Measurement Scales
The topic of measurement scales is one that some writers think is crucial and others think
is irrelevant. Although I tend to side with the latter group, it is important that you have
some familiarity with the general issue. (You do not have to agree with something to think
that it is worth studying. After all, evangelists claim to know a great deal about sin, though
they can hardly be said to advocate it.) An additional benefit of this discussion is that you
will begin to realize that statistics as a subject is not merely a cut-and-dried set of facts but,
rather, a set of facts put together with a variety of interpretations and opinions.
Probably the foremost leader of those who see measurement scales as crucial to the
choice of statistical procedures was S. S. Stevens.^3 Zumbo and Zimmerman (2000) have
discussed measurement scales at considerable length and remind us that Stevens’s system
has to be seen in its historical context. In the 1940s and 1950s, Stevens was attempting to
defend psychological research against those in the “hard sciences” who had a restricted
view of scientific measurement. He was trying to make psychology “respectable.” Stevens
spent much of his very distinguished professional career developing measurement scales
for the field of psychophysics and made important contributions. However, outside of that
field there has been little effort in psychology to develop the kinds of scales that Stevens
pursued, nor has there been much real interest. The criticisms that so threatened Stevens
have largely evaporated, and with them much of the belief that measurement scales criti-
cally influence the statistical procedures that are appropriate.Nominal Scales
In a sense,nominal scalesare not really scales at all; they do not scale items along any di-
mension, but rather label them. Variables such as gender and political-party affiliation are
nominal variables. Such categorical data are usually measured on a nominal scale, because
we merely assign category labels (e.g., male or female; Republican, Democrat, or Indepen-
dent) to observations. A numerical example of a nominal scale is the set of numbers as-
signed to football players. Frequently, these numbers have no meaning other than that they
are convenient labels to distinguish the players from one another. Letters or pictures of ani-
mals could just as easily be used.Ordinal Scales
The simplest true scale is an ordinal scale,which orders people, objects, or events along
some continuum. An excellent example of such a scale is the ranks in the Navy. A com-
mander is lower in prestige than a captain, who in turn is lower than a rear admiral. How-
ever, there is no reason to think that the differencein prestige between a commander and a
captain is the same as that between a captain and a rear admiral. An example from psychol-
ogy would be the Holmes and Rahe (1967) scale of life stress. Using this scale, you count
(sometimes with differential weightings) the number of changes (marriage, moving, new
job, etc.) that have occurred during the past 6 months of a person’s life. Someone who has a
score of 20 is presumed to have experienced more stress than someone with a score of 15,
and the latter in turn is presumed to have experienced more stress than someone with a
score of 10. Thus, people are ordered, in terms of stress, by the number of changes occur-
ring recently in their lives. This is an example of an ordinal scale because nothing is6 Chapter 1 Basic Concepts
(^3) Chapter 1 in Stevens’s Handbook of Experimental Psychology (1951) is an excellent reference for anyone
wanting to examine the substantial mathematical issues underlying this position.
nominal scales
ordinal scale