Level of Measurement Refresher



Just in case you need a refresher on the different levels of measurement, the below three paragraphs are taken directly from Social Statistics for a Diverse Society [2000], by Frankfort-Nachmias and Leon-Guerrero, pg 13-14. [Note this text combines interval level and ratio level variables into one category -  interval-ratio, this module follows that example]



Nominal Level of Measurement  At the nominal level of measurement, numbers or other symbols are assigned to a set of categories for the purpose of naming, labeling, or classifying the observations. Gender is an example of a nominal level variable. Using the numbers 1 and 2, for instance, we can classify our observations into the categories "females" and "males," with 1 representing females and 2 representing males. We could use any of a variety of symbols to represent the different categories of a nominal variable; however, when numbers are used to represent the different categories, we do not imply anything about the magnitude or quantitative difference between the categories.


Ordinal Level of Measurement  Whenever we assign numbers to rank-ordered categories ranging from low to high, we have an ordinal level variable. Social class is an example of an ordinal variable. We might classify individuals with respect to their social class status as "upper class", "middle class", or "working class". We can say that a person in the category "upper class" has a higher class position than a person in a "middle class" category, but we do not know the magnitude of the differences between the categories; that is, we don't know how much higher "upper class" is compared to "middle class".


Interval/Ratio Level of Measurement  If the categories (or values) of a variable can be rank-ordered, and if the measurements for all the cases are expressed in the same units, then an interval-ratio level of measurement has been achieved. Examples of variables measured at the interval-ratio level are age, income, and SAT scores. With all these variables we can compare values not only in terms of which is larger or smaller, but also in terms of how much larger or smaller one is compared with another. In some discussions of levels of measurement you will see a distinction made between interval-ratio variables that have a natural zero point (where zero means the absence of the property) and those variables that have zero as an arbitrary point. For example, weight and length have a natural zero point, whereas temperature has an arbitrary zero point. Variables with a natural zero point are also called ratio variables. In statistical practice, however, ratio variables are subjected to operations that threat them as interval and ignore their ratio properties. Therefore, no distinction between these two types is made in this text.