Renáta Németh, Dávid Simon

ELTE

**Nominal** level of measurement

„Qualitative” variables.

For technical reasons, numbers are often assigned to the categories (Variable gender, 1: male, 2: female)

The assigned numbers are arbitrary; they do not imply anything about the quantitative difference between the categories.

Further examples: party affiliation, religion, ethnicity.

**Ordinal** level of measurement

The categories are ranked, and numbers are often assigned to the categories according to that rank. However, the distance between any two of those numbers does not have a precise numerical meaning.

Example: social class

1: working class, 2: middle class, 3: upper class.

Upper class position is higher than working class position, but it is not three times higher.

Another example: type of settlement.

1: farm, 2: village, 3: town, 4: capital.

The mean (or average) cannot be defined.

**Interval-ratio** level of measurement (or “high” level of measurement)

Examples: age, income, IQ score, temperature.

The distance between any two numbers does have a numerical meaning.

Hence the mean can be defined.

Division cannot be defined.

Examples:

the water of 40^{0}C is not twice as warm as the water of 20^{0}C

a person with 200 IQ scores is not twice as intelligent as a person with 100 IQ

In some discussions of levels of measurement a distinction is made between interval-ratio variables that have a natural zero point (“interval level”: temperature, IQ score) and those variables that have zero as an arbitrary point (“ratio level”: income, age). With ratio level variables we can compare values in terms of how much larger one is compared with another, hence division can be defined.

Usual terminology: Nominal level is the **lowest** level of measurement, while interval level is the **highest**.

IMPORTANT to note:

As we have seen, there are mathematical/statistical operators that can be used only for some of the levels of measurement. An operator applicable for a particular level is applicable for all higher levels as well.

The same concept can be measured on different levels of measurement depending on the aspect of the concept we are interested in.

Nominal

Categories: Private vs. state secondary schoolInterpretation: attended different schools

Ordinal

Categories: secondary school vs. university degree

Interpretation: received higher level of education

Interval

Categories: 8 vs. 16 school grades completed

Interpretation: spent twice as much time attending school

In some cases it is not straightforward whether the variable is measured on ordinal or nominal level. For example: type of settlement (village/town/capital). Level of measurement here depends on the research context.

**Continuous and discrete variables**

**Discrete** variables have a minimum-sized unit of measurement. E.g.: number of patients per GP, unit: one (patient)

**Continuous** variables do not have a minimum-sized unit of measurement; they can take any value (within a range). E.g.: rate of women within active earners (0%-100%).

This attribute of variables affects which statistical operations can be applied to them. However, in practice, some discrete variables with many values are treated as continuous. E.g.: monthly income.