Scales
of Measurement
Statistical
information, including numbers and sets of numbers,
has specific qualities that are of interest to
researchers. These
qualities, including magnitude, equal intervals, and
absolute zero, determine what scale of measurement
is being used and therefore what statistical
procedures are best.
Magnitude refers to the ability to know if
one score is greater than, equal to, or less than
another score. Equal
intervals means that the possible scores are each an
equal distance from each other.
And finally, absolute zero refers to a point
where none of the scale exists or where a score of
zero can be assigned.
When
we combine these three scale qualities, we can
determine that there are four scales of measurement.
The lowest level is the nominal scale, which
represents only names and therefore has none of the
three qualities.
A list of students in alphabetical order, a
list of favorite cartoon characters, or the names on
an organizational chart would all be classified as
nominal data. The
second level, called ordinal data, has magnitude
only, and can be looked at as any set of data that
can be placed in order from greatest to lowest but
where there is no absolute zero and no equal
intervals. Examples
of this type of scale would include Likert Scales
and the Thurstone Technique.
The
third type of scale is called an interval scale, and
possesses both magnitude and equal intervals, but
no absolute zero.
Temperature is a classic example of an interval
scale because we know that each degree is the same
distance apart and we can easily tell if one temperature
is greater than, equal to, or less than another.
Temperature, however, has no absolute zero
because there is (theoretically) no point where temperature
does not exist.
Finally,
the fourth and highest scale of measurement is
called a ratio scale.
A ratio scale contains all three qualities
and is often the scale that statisticians prefer
because the data can be more easily analyzed.
Age, height, weight, and scores on a
100point test would all be examples of ratio
scales. If you are 20 years old, you not only know that you are older
than someone who is 15 years old (magnitude) but you
also know that you are five years older (equal
intervals). With
a ratio scale, we also have a point where none of
the scale exists; when a person is born his or her
age is zero.
Table
8.1: Scales of Measurement
Scale
Level 
Scale
of Measurement 
Scale
Qualities 
Example(s) 
4 
Ratio 
Magnitude
Equal
Intervals
Absolute
Zero 
Age,
Height, Weight, Percentage 
3 
Interval 
Magnitude
Equal
Intervals 
Temperature 
2 
Ordinal 
Magnitude 
Likert
Scale, Anything rank ordered 
1 
Nominal 
None 
Names,
Lists of words 
