46 | S o c i a l S c i e n c e R e s e a r c h
M for male and F for female. Nominal scales merely offer names or labels for different attribute
values. The appropriate measure of central tendency of a nominal scale is mode, and neither
the mean nor the median can be defined. Permissible statistics are chi-square and frequency
distribution, and only a one-to-one (equality) transformation is allowed (e.g., 1=Male,
2=Female).
Ordinal scales are those that measure rank-ordered data, such as the ranking of
students in a class as first, second, third, and so forth, based on their grade point average or test
scores. However, the actual or relative values of attributes or difference in attribute values
cannot be assessed. For instance, ranking of students in class says nothing about the actual GPA
or test scores of the students, or how they well performed relative to one another. A classic
example in the natural sciences is Moh’s scale of mineral hardness, which characterizes the
hardness of various minerals by their ability to scratch other minerals. For instance, diamonds
can scratch all other naturally occurring minerals on earth, and hence diamond is the “hardest”
mineral. However, the scale does not indicate the actual hardness of these minerals or even
provides a relative assessment of their hardness. Ordinal scales can also use attribute labels
(anchors) such as “bad”, “medium”, and “good”, or "strongly dissatisfied", "somewhat
dissatisfied", "neutral", or "somewhat satisfied", and "strongly satisfied”. In the latter case, we
can say that respondents who are “somewhat satisfied” are less satisfied than those who are
“strongly satisfied”, but we cannot quantify their satisfaction levels. The central tendency
measure of an ordinal scale can be its median or mode, and means are uninterpretable. Hence,
statistical analyses may involve percentiles and non-parametric analysis, but more
sophisticated techniques such as correlation, regression, and analysis of variance, are not
appropriate. Monotonically increasing transformation (which retains the ranking) is allowed.
Interval scales are those where the values measured are not only rank-ordered, but are
also equidistant from adjacent attributes. For example, the temperature scale (in Fahrenheit or
Celsius), where the difference between 30 and 40 degree Fahrenheit is the same as that
between 80 and 90 degree Fahrenheit. Likewise, if you have a scale that asks respondents’
annual income using the following attributes (ranges): $0 to 10,000, $10,000 to 20,000, $20,000
to 30,000, and so forth, this is also an interval scale, because the mid-point of each range (i.e.,
$5,000, $15,000, $25,000, etc.) are equidistant from each other. The intelligence quotient (IQ)
scale is also an interval scale, because the scale is designed such that the difference between IQ
scores 100 and 110 is supposed to be the same as between 110 and 120 (although we do not
really know whether that is truly the case). Interval scale allows us to examine “how much
more” is one attribute when compared to another, which is not possible with nominal or ordinal
scales. Allowed central tendency measures include mean, median, or mode, as are measures of
dispersion, such as range and standard deviation. Permissible statistical analyses include all of
those allowed for nominal and ordinal scales, plus correlation, regression, analysis of variance,
and so on. Allowed scale transformation are positive linear. Note that the satisfaction scale
discussed earlier is not strictly an interval scale, because we cannot say whether the difference
between “strongly satisfied” and “somewhat satisfied” is the same as that between “neutral” and
“somewhat satisfied” or between “somewhat dissatisfied” and “strongly dissatisfied”. However,
social science researchers often “pretend” (incorrectly) that these differences are equal so that
we can use statistical techniques for analyzing ordinal scaled data.
Ratio scales are those that have all the qualities of nominal, ordinal, and interval scales,
and in addition, also have a “true zero” point (where the value zero implies lack or non-
availability of the underlying construct). Most measurement in the natural sciences and
engineering, such as mass, incline of a plane, and electric charge, employ ratio scales, as are