Levels of Measurement
Prerequisites
Variables
Learning Objectives
 Define and distinguish among nominal, ordinal, interval, and ratio
scales
 Identify a scale type
 Discuss the type of scale used in psychological measurement
 Give examples of errors that can be made by failing to understand the
proper use of measurement scales
Types of Scales
Nominal scales
When measuring using a nominal scale, one simply
names or categorizes responses. Gender, handedness, favorite color,
and religion are examples of variables measured on a nominal scale.
The essential point about nominal scales is that they do not imply
any ordering among the responses. For example, when classifying
people according to their favorite color, there is no sense in
which green is placed "ahead of" blue. Responses are
merely categorized. Nominal scales embody the lowest level of
measurement.
Ordinal scales
A researcher wishing to measure consumers'
satisfaction with their microwave ovens might ask them to specify
their feelings as either "very dissatisfied," "somewhat
dissatisfied," "somewhat satisfied," or "very
satisfied." The items in this scale are ordered, ranging
from least to most satisfied. This is what distinguishes ordinal
from nominal scales. Whereas nominal scales don't allow comparisons
in the degree to which two subjects possess the dependent variable,
just this kind of comparison is possible with ordinal scales.
On the other hand, ordinal scales fail to capture
important information that will be present in the other scales
we examine. In particular, the difference between two levels of
an ordinal scale cannot be assumed to be the same as the difference
between two other levels.
Interval scales
Interval scales are numerical scales in which
intervals have the same interpretation throughout. As an example,
consider the Fahrenheit scale of temperature. The difference between
30 degrees and 40 degrees represents the same temperature difference
as the difference between 80 degrees and 90 degrees. This is because
each 10 degree interval has the same physical meaning (in terms
of the kinetic energy of molecules).
Interval scales are not perfect, however. In particular,
they do not have a true zero point even if one of the scaled values
happens to carry the name "zero." The Fahrenheit scale
illustrates the issue. Zero degrees Fahrenheit does not represent
the complete absence of temperature (the absence of any molecular
kinetic energy).
Ratio scales
The ratio scale of measurement is the most informative
scale. It is an interval scale with the additional property that
its zero position indicates the absence of the quantity being
measured. You can think of a ratio scale as the three earlier
scales rolled up in one. Like a nominal scale, it provides a name
or category for each object (the numbers serve as labels). Like
an ordinal scale, the objects are ordered (in terms of the ordering
of the numbers). Like an interval scale, the same difference at
two places on the scale has the same meaning. And in addition,
the same ratio at two places on the scale also carries the same
meaning.
What level of measurement is used for psychological
variables?
Rating scales are used frequently in psychological
research. For example, experimental subjects may be asked to rate
their level of pain, how much they like a consumer product, their
attitudes about capital punishment, their confidence in an answer
to a test question. Typically these ratings are made on a 5point
or a 7point scale. These scales are ordinal scales since there
is no assurance that a given difference represents the same thing
across the range of the scale. For example, there is no way to
be sure that a treatment that reduces pain from a rated pain level
of 3 to a rated pain level of 2 represents the same level of relief
as a treatment that reduces pain from a rated pain level of 7
to a rated pain level of 6.
In memory experiments, the dependent variable
is often the number of items correctly recalled. What scale of
measurement is this? You could reasonably argue that it is a ratio
scale. First, there is a true zero point; some subjects may get
no items correct at all. Moreover, a difference of one represents
a difference of one item recalled across the entire scale. It
is certainly valid to say that someone who recalled 12 items recalled
twice as many items as someone who recalled only 6 items.
But numberofitems recalled is a more complicated
case than it appears at first. Consider the following example
in which subjects are asked to remember as many items as possible
from a list of 10. Assume that (a) there are 5 easy items and
5 difficult items, (b) half of the subjects are able to recall
all the easy items and different numbers of difficult items while
(c) the other half of the subjects are unable to recall any of
the difficult items and remember different numbers of easy items.
Some sample data are shown below.
Subject 
Easy Items 
Difficult Items 
Score 
A 
0 
0 
1 
1 
0 
0 
0 
0 
0 
0 
2 
B 
1 
0 
1 
1 
0 
0 
0 
0 
0 
0 
3 
C 
1 
1 
1 
1 
1 
1 
1 
0 
0 
0 
7 
D 
1 
1 
1 
1 
1 
0 
1 
1 
0 
1 
8 
Let's compare (i) the difference between Subject A's score of
2 and Subject B's score of 3 and (ii) the difference between Subject
C's score of 7 and Subject D's score of 8. The former difference
is a difference of one easy item; the latter difference is a difference
of one difficult item. Do these two differences signify the same
difference in memory performance? We are inclined to respond No
to this question since only a little more memory may be needed
to retain the additional easy item whereas a lot more memory may
be needed to retain the additional hard item. The general point
is that it is often inappropriate to consider psychological measurements
scales as either interval or ratio.
Consequences of level of measurement
Why are we so interested in the type of scale
that measures a dependent variable? The crux of the matter is
the relationship between the variable's level of measurement
and the statistics that can be meaningfully computed with that
variable. For example, it is meaningless to compute the mean
of numbers measured on a nominal scale.
Does it make sense to compute the mean of numbers
measured on an ordinal scale? The prevailing (but by no means
unanimous) opinion of statisticians is that for almost all practical
situations, the mean of an ordinallymeasured variable is a meaningful
statistic. However, as you will see in the simulation shown in
the next section, there are extreme situations in which computing
the mean of an ordinallymeasured variable can be very misleading.
