Information Technology Reference
In-Depth Information
CHAPTER TWO
Measurement, Central Tendency,
and Variability
2.1 SCALES OF MEASUREMENT
In Chapter 1, we indicated that variables can take on different values.
Here, we will deal with the process of associating values with variables and
how to summarize the sets of values we obtain from that process. This
will prove to be important in guiding us toward situations in which it is
appropriate to use the ANOVA technique.
2.1.1 THE PROCESS OF MEASUREMENT
Measurement represents a set of rules informing us of how values are
assigned to objects or events. A
scale of measurement
describes a specific
set of rules. Psychology became intimately familiar with scales of measure-
ment when S. S. Stevens, in 1946, wrote a response to a committee of the
British Association for the Advancement of Science. That committee was
dealing with the possibility of measuring sensory events, and the members
could not agree on whether or not it was possible to perform such mea-
surements. Because they had focused on the work that Stevens had done to
measure loudness of sound, he felt that a response to the committee from
him was appropriate. But instead of arguing with the committee, Stevens
adopted a different strategy, presenting instead a theory of measurement.
He elaborated on this theory in 1951 when, as the editor of the
Handbook
of Experimental Psychology,
he gave prominent treatment to this topic in
his lead chapter.
Stevens identified four scales in his theory:
nominal
,
ordinal
,
interval
,
and
ratio
scales in that order. Each scale includes an extra feature or rule
over those in the one before it. We will add a fifth scale to Stevens's
treatment,
summative response scaling
, placing it between the ordinal and
the interval scale.
2.1.2 NOMINAL SCALES
A nominal scale of measurement, sometimes called a
categorical scale
,
qualitative measurement
,or
categorical measurement
, has only one rule
underlying its use: different entities receive different values. This is done
without implying any quantitative dimension at all; that is, there is no
implication that one entity has any more of a property than another.
Examples of nominal scales include numbers on football uniforms, types
9
