Figure 1 presents a graphic illustration of the four levels of measurement. The differences that have been distinguished between the measurement levels have several practical implications, especially in the analysis of collected data, that you need to anticipate in the designing stage of a research. In other words, different measurement levels require particular analytical techniques.
For example, you can plan to report the mean age of the investigated sample of people – calculated by adding up all the individual ages and dividing the sum by the number of people included in the sample – but you cannot plan to report the mean ethnic affiliation, because this is a nominal variable, and the calculation of mean requires a ratio level of measurement. In the latter case, you can only report the modal value, which is the most common ethnic affiliation.
Another important practical aspect is the possibility to operationalize certain variables at different levels of measurement. In this process you should keep in mind that “ratio measures represent the highest level, descending through interval and ordinal to nominal, the lowest level of measurement. A variable representing a higher level of measurement – say, ratio – can also be treated as representing a lower level of measurement – say, ordinal” (Babbie, 2013: 184). Remember that age is a ratio measure. Supposing that by applying a questionnaire, among other collected data, you register the exact age of each respondent and the self-perceived level of happiness, an ordinal-level variable, with three categories: very happy, pretty happy and not too happy. If you intend to explore the relationship between age and happiness, you might also choose to operationalize age as an ordinal-level variable, by dividing the investigated people into three categories: young, middle-aged, and old, indicating the age range compounding each of these groups. In this example, age might be treated as a nominal-level variable to fulfill a certain research purpose. For instance, people might be grouped in two categories – those born until 1989 and those born in 1990 and after that – as the year 1989 is a benchmark in the former Eastern European countries when the political regime changed from communism to democracy. Remember that if you collect the exact age of the participants in research, you can later change this variable into an ordinal or a nominal measure.
Sometimes, you might decide that measuring a variable at its highest level of measurement is not necessary. If you are sure that registering ages of people at higher than the ordinal level of measurement is not needed, you may simply ask people to indicate their corresponding age range by choosing one of the following categories: under 20; 20 to 29; 30 to 39, and so forth. Just be attentive to construct equal, mutually exclusive age ranges and covering all possible age values.
Some variables are limited to a certain level of measurement, such as marital status, gender, or race, so you can only gather data about these variables as nominal measures. However, when a variable can be measured at different measurement levels, and when your research purpose is not well-defined at the beginning of research, the best way is to collect data about variables at their highest level of measurement possible. Keep in mind that ratio measures can later be transformed into ordinal or nominal groupings, but you cannot convert ordinal measures into ratio. Generally speaking, you cannot convert a lower-level measure to a higher-level one.
Levels of measurement are significant in terms of statistical techniques that use arithmetic operations. Table 1 summarizes these distinctions, using as example temperature as an interval variable.
Table 1. Arithmetic operations associated with levels of measurement
Level of measurement |
Arithmetic operations |
Temperature |
Nominal |
= ≠ |
Winter is not like summer. |
Ordinal |
> < |
Today was colder than yesterday. |
Interval |
+ ‒ |
Today was 4 degrees colder than yesterday. |
Ratio |
÷ × |
Today was twice as cold than yesterday. |
Note: In the case of Fahrenheit and Celsius scales, these comparisons can be made at the nominal, ordinal and interval levels of measurement, as both of them have a zero point which is established arbitraryly. Instead, for Kelvin scale, all these comparisons are correct, as this scale is based on an absolute zero, which means a complete lack of heat.