Chapter 1 Variables and Their Measurement
1.4 Level of Measurement and Operationalization Considerations
All in all, the difference between interval and ratio variables exists more on a conceptual level rather than in practical terms. As such, they are frequently grouped together in an interval/ratio category and treated the same for the purposes of statistical analysis. At this stage, while it’s preferable to know the difference between them, it is still far more important to be able to differentiate interval/ratio variables from nominal and ordinal ones.
Here is proof how tricky identifying the correct level of measurement of a variable can be.
Watch Out!! #1 … for Likert Scales
Most likely, at some point you have encountered survey questions that read something like this:
“On a scale of 1 to 5, where 1 is the lowest and 5 is the highest, how much do you like …?”
… let’s say, “chocolate”. It is possible that you were presented with the numbers from 1 to 5 to choose from, or that they were accompanied with phrasing of the strongly dislike, dislike, neither like nor dislike, like, strongly like type. Now that you know about levels of measurement, as what scale would you classify the variable liking of chocolate: nominal, ordinal, or interval/ratio?
Considering that the answers from which one can choose are listed as numbers, many students are tempted to classify such a variable is interval. However, the strongly dislike, dislike, neither like nor dislike, like, strongly like part should give you more clues. Ask yourself: is there a uniform unit that allows us to precisely measure the “distance” between dislike and strongly dislike? Or between like and neither like nor dislike? Is it even the same “distance”? We would be hard-pressed to say “yes” to any of these questions. We know that people who like chocolate like it more than those who neither like it nor dislike it but we don’t know exactly how much more. The numbers are there to make analyzing the responses easier, and as a sort of “code” for the ranking of preferences regarding chocolate, but substantively the ranking contains only order, not precise measurement of these preferences.
Variables such as these are called Likert scales. As I just explained, they are ordinal by constitution (although, in some special cases — for example, when the possible responses are not five but, say, ten or more — they can be treated as interval for purposes of analysis). Researchers use them usually to capture people’s preferences — but preferences are generally “fuzzy” and not fully-defined; they do not come with a build-in, measurable, uniform unit scale, despite the fact that it seems like the numbers represent one such scale.
In Chapter 2 you will see that numbers can be used to represent a lot more than actual numbers. (And you were just starting to think identifying the level of measurement is easy!)
A further word of caution: the examples I used in this chapter might leave you with the impression that you can simply hear the name of a variable and you should be able to identify its scale of measurement. That would be wrong. My examples are hypothetical and as such I imagine what the variables’ categories might look like. (I also ask you to imagine variables and their categories in the Do It! exercises.) However, variables — not hypothetical, real variables that we use for analysis — exist in real datasets, where they have been operationalized in one specific, concrete way.
As such, upon hearing the name of a variable, instead of imagining what it looks like, you should always – always! – actually look at it and its categories in the given/specific dataset of which the variable is a part. Determining an existing variable’s scale of measurement requires exploring the actual variable as it was created. Recall that there is more than one way to operationalize a variable. Thus, the researcher/s who created some variable into which you might be looking might arguably have created it differently than you would, or differently than some other researchers might have created theirs — even if these variables (the different researchers’ and your hypothetical one) have the same name.
This leads us to the question: Can the same concept be operationalized at different levels of measurement? The answer lies in the nature of the concept (or that of the hypothetical variable, if you prefer). Let’s go back to the example of income from the previous section on operationalization. There I provided you with a few different ways to create income categories. One was based on a yes/no question (“Is your income below…?” a specific number), and few more ways listed several categories based on income groups (“0-19,999”, “20,000-29,999”,….etc.). Additionally, we could ask people to supply their specific income, rounded to the nearest dollar. Alternatively, thinking along the lines of a survey questions, this would result in a) yes/no response, b) multiple choice answer, and lastly, c) an open-ended, respondent-supplied answer.
In this way, we can say that we can successfully operationalize the concept of income at three different levels of measurement: a) nominal, b) ordinal, and c) ratio, respectively. This is only possible because of the numerical nature of income: income is monetary, and money is countable – and expressed in numbers. We can choose to create several categories of income (out of the numbers involved), or we could choose to create only a binary variable (i.e., with two categories) to indicate an income below/above some threshold. In choosing either of these, we also make the decision to forego, or lose the more specific information of the actual income of everyone we ask. Logically though, we can only forego/lose information that is otherwise potentially available: we cannot make information up.
What it all boils down to is that we can operationalize down: from the highest level of measurement possible for a variable towards the lower ones – but never vice versa. A concept of numerical nature, i.e., an interval/ratio variable can be operationalized down and created as an ordinal variable, or even further down as a nominal variable, losing potential information (actual numbers and order) along the way. A concept of ordinal nature can also be operationalized down to a nominal scale, again, foregoing the potential information of order. However, a “naturally” nominal variable cannot be operationalized as anything else but nominal: there is simply no further information available. The same goes for “naturally” ordinal variables – they cannot be operationalized as interval/ratio as the only information we can have is order, while precision and measurable, defined constant units are not possible to obtain.[1]
- Beyond the original operationalization, sometimes researchers actually recode variables down within an existing dataset. Since they start with an interval/ratio variable, they can choose which level of measurement they want to use, and go back and forth between ordinal and nominal and back to interval/ratio. They can do this only because the information has initially been collected at interval/ratio level of detail. If the original information is collected as nominal or ordinal data, no further information cannot be accessed: recoding up is impossible. ↵