# 18 5.3 Levels of measurement

### Learning Objectives

- Define and provide examples for the four levels of measurement

Now that we have figured out how to define, or conceptualize, our terms we’ll need to think about operationalizing them. **Operationalization** is the process by which researchers *conducting quantitative research* spell out precisely how a concept will be measured. It involves identifying the specific research procedures we will use to gather data about our concepts. This of course requires that we know what research method(s) we will employ to learn about our concepts, and we’ll examine specific research methods later on in the text. For now, let’s take a broad look at how operationalization works. We can then revisit how this process works when we examine specific methods of data collection in later chapters. Remember, operationalization is only a process in quantitative research. Measurement in qualitative research will be discussed at the end of this section.

# Levels of measurement

** **When social scientists measure concepts, they sometimes use the language of variables and attributes (also called *values*). A **variable** refers to a phenomenon that can vary. It can be thought of as a grouping of several characteristics. For example, hair color could be a variable because it has varying characteristics. **Attributes** are the characteristics that make up a variable. 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. The latter two levels of measurement are **continuous**, meaning their attributes are numbers, not categories.

## Nominal level of measurement

Hair color is an example of a nominal level of measurement. **Nominal** measures are categorical, and those categories cannot be mathematically ranked. There is no ranking order between hair colors. They are simply different. That is what constitutes a nominal level of measurement. Gender and race are also measured at the nominal level.

When using nominal level of measurement in research, it is very important to assign the attributes of potential answers very precisely. The attributes need to be *exhaustive* and *mutually exclusive*. Let’s think about the attributes contained in the variable* hair color*. Black, brown, blonde, and red are common colors. But, if we listed only these attributes, people with gray hair wouldn’t fit anywhere. That means 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 trying to achieve exhaustiveness can get to be too much. 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 could 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 list of attributes like *all black*, *all brown*, *all blonde*, *all red*, *multi-color, other *to include people with more than one hair color, but keep everyone in only one category.

The discussion of hair color elides an important point with measurement—reification. You should remember reification from our previous discussion in this chapter. 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. We shouldn’t confuse our labeling of attributes or measuring of a variable with the objective truth “out there.” Another example could be children of parents from different races were often classified as one race or another in the past, 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 level of measurement

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 one being the lowest and 5 being the highest, how likely are you to recommend our company to other people?” Sound 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 could 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.

## Interval level of measurement

At the **interval **level, the distance between attributes is known to be equal. Interval measures are also continuous, 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. But we can say it is 50 degrees cooler than 100. At the interval level, attributes must also be exhaustive and mutually exclusive.

## Ratio level of measurement

Finally, at the **ratio **level, 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, for example, that a person who is 12 years old is twice as old as someone who is 6 years old. Just like all other levels of measurement, at the ratio level, attributes must be mutually exclusive and exhaustive.

The differences between each level of measurement are visualized in Table 5.1.

Nominal | Ordinal | Interval | Ratio | |

Exhaustive | X | X | X | X |

Mutually exclusive | X | X | X | X |

Rank-ordered | X | X | X | |

Equal distance between attributes | X | X | ||

Can compare ratios of the values (e.g., twice as large) | X | |||

True zero point | X |

### Key Takeaways

- In social science, our variables can be one of four different levels of measurement: nominal, ordinal, interval, or ratio.

### Glossary

- Categorical measures- a measure with attributes that are categories
- Continuous measures- a measures with attributes that are numbers
- Exhaustiveness- all possible attributes are listed
- Interval level- a level of measurement that is continuous, can be rank ordered, is exhaustive and mutually exclusive, and for which the distance between attributes is known to be equal
- Likert scales- ordinal measures that use numbers as a shorthand (e.g., 1=highly likely, 2=somewhat likely, etc.) to indicate what attribute the person feels describes them best
- Mutual exclusivity- a person cannot identify with two different attributes simultaneously
- Nominal- level of measurement that is categorical and those categories cannot be mathematically ranked, though they are exhaustive and mutually exclusive
- Ordinal- level of measurement that is categorical, those categories can be rank ordered, and they are exhaustive and mutually exclusive
- Ratio level- level of measurement in which attributes are mutually exclusive and exhaustive, attributes can be rank ordered, the distance between attributes is equal, and attributes have a true zero point
- Variable- refers to a grouping of several characteristics