Types of Variables

In quantitative data, our whole goal of measuring the things we do (the constructs) is to obtain variables. Variables, like we’ve discussed before, are what they sound like: characteristics that vary among participants. Things that don’t vary at all, like the number of seconds in a minute, or that don’t vary among our particular research participants, such as sex if we only recruited a sample of biological females, are not variables (those are, conversely, constants). Because they don’t vary, they don’t actually tell us much useful information for our study. The basic idea in most quantitative research is looking for patterns in the variability of the construct of interest: is self-confidence different between men and women? Does marital quality change over the first five years of a marriage? Do boys who get sent to the principal’s office have lower grades than those who don’t? How many dating couples discuss contraception within the first two months of their relationship? Whatever we’re looking at, the variability is most often key.

Thus, whatever measurement we’re using needs to be able to detect differences. Different kinds of variables provide different information, though, and it’s important to be able to recognize what a variable can tell us and, just as importantly, what it cannot. Variables are made up of attributes. For example, the variable hair color would contain attributes like blonde, brown, black, red, gray, etc. A variable’s attributes determine its level of measurement. There are four possible levels of measurement: nominal, ordinal, interval, and ratio. The first two levels of measurement are categorical, meaning their attributes are categories rather than numbers – although they’ll have numbers assigned, we can’t do the same things with those numbers that we normally would. The latter two levels of measurement are continuous, meaning their attributes are numbers and can be treated as such. The level of measurement that a variable embodies influences what kinds of analysis can be done on it, and what information can be taken from it.

Nominal 

Hair color is an example of a nominal level of measurement. Nominal measures are categorical, and those categories cannot be mathematically ranked (that is, one is not “more” than another). No matter how much you might like having whatever hair color you have, can you say with certainty that your hair color is “better” than another? As with all nominal levels of measurement, there is no ranking order between hair colors; they are simply different. Gender and race are also measured at the nominal level, and you can likely think of many other categories that don’t have an order to them.

What attributes are contained in the variable hair color? While blonde, brown, black, and red are common colors, some people may not fit into these categories if we only list these attributes. What about someone with purple hair? What about someone who is bald? If we had this question with these attributes listed on a survey, respondents with purple hair, no hair, or grey hair may not be able to answer the question! This means that our attributes were not exhaustive. Exhaustiveness means that all possible attributes are listed. We may have to list a lot of colors before we can meet the criteria of exhaustiveness. Clearly, there is a point at which exhaustiveness has been reasonably met. If a person insists that their hair color is light burnt sienna, it is not your responsibility to list that as an option. Rather, that person would reasonably be described as brown-haired. Perhaps listing a category for other color would suffice to make our list of colors exhaustive.

What about a person who has multiple hair colors at the same time, such as red and black? They would fall into multiple attributes. This violates the rule of mutual exclusivity, in which a person cannot fall into two different attributes. Instead of listing all of the possible combinations of colors, perhaps you might include a multi-color attribute to describe people with more than one hair color.

The discussion of hair color elides an important point with measurement—reification. You should remember reification from our previous discussions about measurement. For many years, the attributes for gender were male and female. Now, our understanding of gender has evolved to encompass more attributes including transgender, non-binary, or genderqueer. Children of parents from different races were often classified as one race or another, even if they identified with both cultures equally. The option for bi-racial or multi-racial on a survey not only more accurately reflects the racial diversity in the real world but validates and acknowledges people who identify in that manner.

Ordinal

Unlike nominal-level measures, attributes at the ordinal level can be rank ordered. For example, someone’s degree of satisfaction in their romantic relationship can be ordered by rank. That is, you could say you are not at all satisfied, a little satisfied, moderately satisfied, or highly satisfied. Note that even though these have a rank order to them (not at all satisfied is certainly worse than highly satisfied), we cannot calculate a mathematical distance between those attributes. We can simply say that one attribute of an ordinal-level variable is more or less than another attribute.

This can get a little confusing when using Likert scales. If you have ever taken a customer satisfaction survey or completed a course evaluation for school, you are familiar with Likert scales. “On a scale of 1-5, with 1 being the lowest and 5 being the highest, how likely are you to recommend our company to other people?” That surely sounds familiar. Likert scales use numbers, but only as a shorthand, to indicate what attribute (highly likely, somewhat likely, etc.) the person feels describes them best. You wouldn’t say you are “2 more likely” to recommend the company, but you would say you are not very likely to recommend the company. Ordinal-level attributes must also be exhaustive and mutually exclusive, as with nominal-level variables.

As mentioned before, nominal and ordinal variables are categorical. Although we usually have to assign a number to each attribute (marital status, as an example of a nominal variable, might be 1 = married, 2 = engaged, 3 = single), we can’t treat those numbers like we usually would (we can’t subtract “married” from “single” to get “engaged”, for example). Instead, the numbers do denote the categories, and maybe even order the categories as we just saw with ordinal variables, but don’t try to do anything too fancy with them.

Interval 

At the interval level, attributes must also be exhaustive and mutually exclusive and there is equal distance between attributes. Interval measures are also continuous (as opposed to categorical), meaning their attributes are numbers, rather than categories. IQ scores are interval level, as are temperatures. Interval-level variables are not particularly common in social science research, but their defining characteristic is that we can say how much more or less one attribute differs from another. We cannot, however, say with certainty what the ratio of one attribute is in comparison to another. For example, it would not make sense to say that 50 degrees is half as hot as 100 degrees Fahrenheit.

Ratio

Finally, at the ratio level, attributes are mutually exclusive and exhaustive, attributes can be rank ordered, the distance between attributes is equal, and attributes have a true zero point. Thus, with these variables, we can say what the ratio of one attribute is in comparison to another. Examples of ratio-level variables include age and years of education. We know that a person who is 12 years old is twice as old as someone who is 6 years old. The differences between each level of measurement are visualized below:

Using variables of different types

So what does this mean for you, or any quantitative researcher? It means that for each variable you hope to analyze, you must first consider what level of measurement it uses. If it’s a categorical variable, that will limit what kinds of mathematical techniques will make sense on it – for example, if you are measuring homeownership as a nominal variable (owner, renter, live with family, unhoused), then it doesn’t make sense to calculate an average value from those numbers. On the other hand, some visualization methods make more and less sense for different types of variables or some variables might require certain visualization decisions to make them interpretable. Keep this in mind as we discuss descriptive statistics and visualizations, and if you go on to more advance statistical training, you’ll become very familiar with the limitations and work-arounds of different levels of measurement.