# Levels of measurement: Nominal, ordinal, interval, ratio

Levels of measurement, also called scales of measurement, tell you how precisely variables are recorded. In scientific research, a variable is anything that can take on different values across your data set (e.g., height or test scores).

There are 4 levels of measurement:

• Nominal: the data can only be categorised
• Ordinal: the data can be categorised and ranked
• Interval: the data can be categorised, ranked, and evenly spaced
• Ratio: the data can be categorised, ranked, evenly spaced, and has a natural zero.

Depending on the level of measurement of the variable, what you can do to analyse your data may be limited. There is a hierarchy in the complexity and precision of the level of measurement, from low (nominal) to high (ratio).

## Nominal, ordinal, interval, and ratio data

Going from lowest to highest, the 4 levels of measurement are cumulative. This means that they each take on the properties of lower levels and add new properties.

Nominal level Examples of nominal scales
You can categorise your data by labelling them in mutually exclusive groups, but there is no order between the categories.
• City of birth
• Gender
• Ethnicity
• Car brands
• Marital status
Ordinal level Examples of ordinal scales
You can categorise and rank your data in an order, but you cannot say anything about the intervals between the rankings.

Although you can rank the top 5 Olympic medallists, this scale does not tell you how close or far apart they are in number of wins.

• Top 5 Olympic medallists
• Language ability (e.g., beginner, intermediate, fluent)
• Likert-type questions  (e.g., very dissatisfied to very satisfied)
Interval level Examples of interval scales
You can categorise, rank, and infer equal intervals between neighboring data points, but there is no true zero point.

The difference between any two adjacent temperatures is the same: one degree. But  zero degrees is defined differently depending on the scale – it doesn’t mean an absolute absence of temperature.

The same is true for test scores and personality inventories. A zero on a test is arbitrary; it does not mean that the test-taker has an absolute lack of the trait being measured.

• Test scores (e.g., IQ or exams)
• Personality inventories
• Temperature in Fahrenheit or Celsius
Ratio level Examples of ratio scales
You can categorise, rank, and infer equal intervals between neighboring data points, and there is a true zero point.

A true zero means there is an absence of the variable of interest. In ratio scales, zero does mean an absolute lack of the variable.

For example, in the Kelvin temperature scale, there are no negative degrees of temperature – zero means an absolute lack of thermal energy.

• Height
• Age
• Weight
• Temperature in Kelvin

## Why are levels of measurement important?

The level at which you measure a variable determines how you can analyse your data.

The different levels limit which descriptive statistics you can use to get an overall summary of your data, and which type of inferential statistics you can perform on your data to support or refute your hypothesis.

In many cases, your variables can be measured at different levels, so you have to choose the level of measurement you will use before data collection begins.

## Which descriptive statistics can I apply on my data?

When measuring the central tendency or variability of your data set, your level of measurement decides which methods you can use based on the mathematical operations that are appropriate for each level.

The methods you can apply are cumulative; at higher levels, you can apply all mathematical operations and measures used at lower levels.

Data type Mathematical operations Measures of central tendency Measures of variability
Nominal
• Equality (=, ≠)
• None
Ordinal
• Equality (=, ≠)
• Comparison (>, <)
Interval
• Equality (=, ≠)
• Comparison (>, <)
Ratio
• Equality (=, ≠)
• Comparison (>, <)
• Multiplication, division (×, ÷)
• Mode
• Median
• Arithmetic mean
• *Geometric mean
• Range
• Interquartile range
• Standard deviation
• Variance
• **Relative standard deviation

## Quiz: Nominal, ordinal, interval, or ratio?

How do I decide which level of measurement to use?

Some variables have fixed levels. For example, gender and ethnicity are always nominal level data because they cannot be ranked.

However, for other variables, you can choose the level of measurement. For example, income is a variable that can be recorded on an ordinal or a ratio scale:

• At an ordinal level, you could create 5 income groupings and code the incomes that fall within them from 1–5.
• At a ratio level, you would record exact numbers for income.

If you have a choice, the ratio level is always preferable because you can analyse data in more ways. The higher the level of measurement, the more precise your data is.

Why do levels of measurement matter?

The level at which you measure a variable determines how you can analyse your data.

Depending on the level of measurement, you can perform different descriptive statistics to get an overall summary of your data and inferential statistics to see if your results support or refute your hypothesis.

What are the four levels of measurement?

Levels of measurement tell you how precisely variables are recorded. There are 4 levels of measurement, which can be ranked from low to high:

• Nominal: the data can only be categorised.
• Ordinal: the data can be categorised and ranked.
• Interval: the data can be categorised and ranked, and evenly spaced.
• Ratio: the data can be categorised, ranked, evenly spaced and has a natural zero.

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