QUALITATIVE AND QUANTITATIVE MEASUREMENTin Kelvin. The Kelvin scale has an absolute zero (the
absence of all heat), and its ratio corresponds to
physical conditions. While this physical world
example may be familiar, another example of arbi-
trary—not true—zeros occurs when measuring atti-
tudes with numbers. We may assign a value to
statements in a survey questionnaire (e.g., –1 =
disagree, 0 = no opinion, +1 = agree). Just because
our data are in the form of numbers does not allow
us to use statistical procedures that require the
mathematical assumption of a true zero.
Discrete variables are nominal and ordinal,
whereas we can measure continuous variables at the
interval or ratio level. There is an interesting unidi-
rectional relationship among the four levels. We can
convert a ratio-level measure into the interval,
ordinal, or nominal level; an interval level into an
ordinal or nominal level; and an ordinal into a
nominal level; but the process does not work in the
opposite way! This happens because higher levels
of measurement contain more refined information
than lower levels. We can always toss out or ignore
the refined information of a high-level measure, but
we cannot squeeze additional refined information
out of a low-level measure.
For ordinal measures, we generally want to
have at least five ordinal categories and try to ob-
tain many observations for each. This is so because
a distortion occurs as we collapse a continuous
construct into few ordered categories. We minimize
the distortion as the number of ordinal categories
and the number of observations increase.^15 (See
Example Box 2, Example of Four Levels of
Measurement).
Before continuing, keep two things in mind.
First, we can measure nearly any social phenome-
non. We can measure some constructs directly and
create precise numerical values (e.g., family in-
come) while other constructs are less precise and
require the use of surrogates or proxies to indirectly
measure a variable (e.g., predisposition to commit
a crime). Second, we can learn a great deal from the
measures created by other researchers. We are for-
tunate to have the work of other researchers to draw
on. It is not always necessary to start from scratch.
We can use a past scale or index or modify it for our
own purposes. Measuring aspects of social life is an
ongoing process. We are constantly creating ideas,
refining theoretical definitions, and improving mea-
sures of old or new constructs.EXAMPLE BOX 2
Example of Four Levels of MeasurementVARIABLE (LEVEL
OF MEASUREMENT) HOW VARIABLE IS MEASURED
Religion (nominal) Different religious denominations (Jewish, Catholic, Lutheran, Baptist) are not
ranked but are only different (unless one belief is conceptualized as closer to
heaven).
Attendance (ordinal) “How often do you attend religious services? (0) Never, (1) less than once a year,
(3) several times a year, (4) about once a month, (5) two or three times a week, or
(8) several times a week.” This might have been measured at a ratio level if the exact
number of times a person attended were asked instead.
IQ score (interval) Most intelligence tests are organized with 100 as average, middle, or normal. Scores
higher or lower indicate distance from the average. Someone with a score of 115 has
somewhat above average measured intelligence for people who took the test,
whereas 90 is slightly below. Scores of below 65 or above 140 are rare.
Age (ratio) Age is measured by years. There is a true zero (birth). Note that a 40-year-old has
lived twice as long as a 20-year-old.