The
level of measurement refers to the relationship among the values that are
assigned to the attributes for a variable. What does that mean? Begin with the
idea of the variable, in this example "party affiliation." That
variable has a number of attributes. Let's assume that in this particular
election context the only relevant attributes are "republican",
"democrat", and "independent". For purposes of
analyzing the results of this variable, we arbitrarily assign the values 1, 2
and 3 to the three attributes.
The level of measurement describes
the relationship among these three values. In this case, we simply are using
the numbers as shorter placeholders for the lengthier text terms. We don't
assume that higher values mean "more" of something and lower numbers
signify "less". We don't assume the the value of 2 means that
democrats are twice something that republicans are. We don't assume that
republicans are in first place or have the highest priority just because they
have the value of 1. In this case, we only use the values as a shorter name for
the attribute. Here, we would describe the level of measurement as
"nominal".
Why is Level of Measurement
Important?
First, knowing the level of measurement helps you
decide how to interpret the data from that variable. When you know that a
measure is nominal (like the one just described), then you know that the
numerical values are just short codes for the longer names. Second, knowing the
level of measurement helps you decide what statistical analysis is appropriate
on the values that were assigned. If a measure is nominal, then you know that
you would never average the data values or do a t-test on the data.
There are typically four levels of measurement that
are defined:
- Nominal
- Ordinal
- Interval
- Ratio
In nominal measurement the numerical values just "name"
the attribute uniquely. No ordering of the cases is implied. For example,
jersey numbers in basketball are measures at the nominal level. A player with
number 30 is not more of anything than a player with number 15, and is
certainly not twice whatever number 15 is.
In ordinal measurement
the attributes can be rank-ordered. Here, distances between attributes do not
have any meaning. For example, on a survey you might code Educational
Attainment as 0=less than H.S.; 1=some H.S.; 2=H.S. degree; 3=some college;
4=college degree; 5=post college. In this measure, higher numbers mean more education.
But is distance from 0 to 1 same as 3 to 4? Of course not. The interval between
values is not interpretable in an ordinal measure.
In interval measurement the distance between attributes does have meaning. For example, when we measure
temperature (in Fahrenheit), the distance from 30-40 is same as distance from
70-80. The interval between values is interpretable. Because of this, it makes
sense to compute an average of an interval variable, where it doesn't make
sense to do so for ordinal scales. But note that in interval measurement ratios
don't make any sense - 80 degrees is not twice as hot as 40 degrees (although
the attribute value is twice as large).
Finally, in ratio measurement
there is always an absolute zero that is meaningful. This means that you can
construct a meaningful fraction (or ratio) with a ratio variable. Weight is a
ratio variable. In applied social research most "count" variables are
ratio, for example, the number of clients in past six months. Why? Because you
can have zero clients and because it is meaningful to say that "...we had
twice as many clients in the past six months as we did in the previous six
months."
It's
important to recognize that there is a hierarchy implied in the level of
measurement idea. At lower levels of measurement, assumptions tend to be less
restrictive and data analyses tend to be less sensitive. At each level up the
hierarchy, the current level includes all of the qualities of the one below it
and adds something new. In general, it is desirable to have a higher level of
measurement (e.g., interval or ratio) rather than a lower one (nominal or
ordinal).
