In statistics, all variables are measured on one of four measurement scales:
- Nominal: Variables that have no quantitative values.
- Ordinal: Variables that have a natural order, but no quantifiable difference between values.
- Interval: Variables that have a natural order and a quantifiable difference between values, but no “true zero” value.
- Ratio: Variables that have a natural order, a quantifiable difference between values, and a “true zero” value.
The following graphic summarizes these different levels of measurement:
One question students often have is:
Is “age” considered an interval or ratio variable?
The short answer:
Age is considered a ratio variable because it has a “true zero” value.
It’s possible for an individual to be zero years old (a newborn) and we can say that the difference between 0 years and 10 years is the same as the difference between 10 years and 20 years.
Since age is a ratio variable, we can also say that someone who is 10 years old is twice as old as someone who is 5 years old.
Contrast this with an interval variable like temperature: We cannot say that 10 degrees Celsius is twice as warm as 5 degrees Celsius because there is no “true zero” when it comes to temperature since degrees can be negative.
When is Age Not a Ratio Variable?
The only time that age would not be considered a ratio variable is if the data we collect on age is in categories.
For example, we may send out a survey and ask people to report which age bracket they belong in from the following choices:
- 0-19 years old
- 20-39 years old
- 40-59 years old
- 60+ years old
In this scenario, age would be treated as an ordinal variable because a natural order exists among the potential values.
We would say 0-19 years old is younger than 20-39 years old, which is younger than 40-50 years old, which is younger than 60+ years old.
We would not classify age as a ratio variable in this scenario because we can’t say with certainty that someone in the 20-39 years old group is twice as old as someone in the 0-19 years age group since we don’t know exact ages.
This represents a rare scenario where we would not classify age as a ratio variable.
Levels of Measurement: Nominal, Ordinal, Interval and Ratio
Is Age a Discrete or Continuous Variable?
Categorical vs. Quantitative Variables