Measurement Scales
Dr. Bob Kizlik
December 21, 2014
If you have read the information on the
ADPRIMA page on measurement, assessment and evaluation in education,
and arrived at this page, you are in the right place. This page
was added several years after the aforementioned page was included
on my site. The reason for this page is to provide you with a
little bit of clarification and an expansion of the understandings I
hope you gleaned from the page on measurement, assessment and
evaluation.
Basically, any time a measurement is
made we are looking at an object or condition that meets certain
criteria for inclusion or exclusion from descriptive sets. These
sets are what I refer to as measurement scales. So if you will
indulge me,
I will provide a description of these scales so that your
understanding of what they mean and how they are used in statistical
analysis may be improved.
There are four basic measurement scales.
From least complex to most complex, they are: nominal, ordinal,
interval, and ratio. They are fundamental to the process of
measurement, and without an understanding of their differences, at
best poor information will be derived, and at worse, erroneous
conclusions will be reached.
The measurement scale descriptions:
Nominal measurement scales refer
to those measurements when the only meaningful results are the
delineations that one thing is different from another. For example,
if you have a bag of apples and a bucket of coal, the only
measurement possible involves the nominal scale. All you can say is
that one set is apples and the other set is coal. It is a measurement
where the only conclusion you can reach is that one thing is
different from another. Another way to consider the nominal
measurement scale is to think of it as a basic classification
system. It might also be worthwhile to take a look at the behavioral
verb "classify." In
the nominal scale you are essentially classifying by name. It is
always a good idea to be as clear as possible when doing this.
Ordinal measurement scales refer
to those measurements where the results indicate only that one thing
is either greater or lesser than another. This always means a
measurement that explicitly implies that the objects, events or
processes and be placed into some order. The assigning of grades
based on scores is an example of this scale, with, for example, the
observation that a grade of "A" represents not only a different
value than a grade of "C" but that it also represents a higher or
greater value.
Interval measurement scales refer
to those measurements where there are equal intervals between given
values. Interval scales are used in almost every aspect of common
measurement. A ruler employs an interval scale. That means that the
distance between three inches and six inches is the same as the
distance between nine inches and twelve inches. In a room
thermometer, the difference in degrees between 72 Fahrenheit and 78
Fahrenheit is the same as that between 90 degrees Fahrenheit and
96 degrees. The intervals are the same.
Ratio measurement scales are
the same as ordinal scales with one important difference. The
difference is that ratio measurement scales contain a zero.
the inclusion of a zero allows for negative values to be expressed
in relation to a positive value. The most obvious and easily
understood example of a ratio measurement scale is an outdoor
thermometer. The intervals are equal, but whether Fahrenheit or
Celsius, measurement values can be expressed as a negative, as in
10 degree Celsius.
So there in a nutshell you have it.
Measurement always involves some sort of scale, and the observations
linked to the measurements can be noted as a simple difference of
name and thus a simple classification. One step up in complexity is
the ordinal scale which implies the there is an order to the object
or process, and one thing can be said to be not just different, but
greater or lesser than another. The next up in cmplexity, the interval scale is the most
frequently used for measurement and rests on the certainty of equal
intervals between sequential points on the scale. Finally
there are ratio scales, which are exactly like interval scales with
the addition of a zero point.
This is provided to give a little
perspective on the description of educational measurement.
Click here to
return to the page on educational measurement, assessment and
evaluation.
