# Levels of Measurement – Meaning & Examples

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Levels of measurement is a classification system used in scientific research, to describe the nature of variables in data sets.

In this article, you will find out more about the four levels used and why their use is now considered so important when recording both qualitative and quantitative data sets.

## Levels of Measurement – In a Nutshell

Given that a variable is anything that can take on different values in a set of data, there are numerous different classes of measurement levels that describe them.

Most commonly, four types – or scales – are used to classify levels of measurement within data sets, a system pioneered by the American psychologist, SS Stevens, in the 1940s:1

Each classification – or level – helps to make it easier to understand the type of variables in data sets and, therefore, how they can be analyzed.

## Definition: Levels of measurement

The definition of levels of measurement – also sometimes called the scale of measure – is an approach to statistics that helps to organize data sets according to the sort of variables that are contained within them.

Identifying the level means being able to apply the most appropriate statistical techniques thereafter.

For example, this model allows purely numerical data sets (e.g. the height of trees in meters) to be compared to non-numerical data sets (e.g. the day of the year when tree blossom first appears).

As mentioned, there are usually four levels of measurement according to the common Stevens definition but other approaches exist, notably a system developed by Frederick Mosteller and John Tukey.2

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## Types of measurement levels

To better understand why scientific researchers use levels of measurement, it is helpful to examine the four most common levels in turn.

#### Nominal level

The nominal level of measurement is regarded as the lowest on the scale. In it, data variables can only be categorized.

Examples of nominal-level variables in a data set would be:

• someone’s gender
• their place of birth
• the country they reside in

#### Ordinal level

The ordinal level of measurement is regarded as the second-lowest on the scale. In it, data variables can be ranked as well as categorized.

Examples of ordinal-level variables in a data set would be:

• the top ten longest-serving prime ministers
• someone’s skiing ability (e.g. beginner, intermediate, or advanced)
• where on a scale someone says they’d be likely to recommend a service

#### Interval level

The interval level of measurement is regarded as the second-highest on the scale. In it, data variables can be evenly spaced as well as ranked and categorized.

Examples of interval-level variables in a data set would be:

• the temperature in °C, recorded at hourly intervals during the day
• what scores a group of individuals achieves following an IQ or self-assessed personality test3

#### Ratio level

The ratio level of measurement is regarded as the highest on the scale. In it, data variables can be evenly spaced as well as ranked and categorized just like the interval level.

In addition, it will also contain a true zero. In this sense, true zero means that a variable could equal zero rather than the absence of a result. For example, when measuring people’s shoe sizes, no one will have a zero-sized shoe.

However, if the data set was drawn from a survey of how many shoes people own, a true zero result could be possible.

Examples of ratio-level variables in a data set would be:

• the height of a person
• their weight
• their age
• the temperature recorded in Kelvins (K)

## Levels of measurement: Descriptive statistics

Descriptive statistics apply in levels of measurement. Their purpose is to assist when a measurement of variable spread or central tendency is being sought.4

In terms of levels of measurement, descriptive statistics means being able to obtain a swift idea of where the middle of the data set might be. This is the aforementioned central tendency to give it its mathematical term. Equally, the spread of variables in a given data set can be more easily determined when levels of measurement are applied.

In this sense, spread really means variability – how low or how high a variable might be given the set of data under examination.

 Level of measurement Middle tendency Spread type Nominal Mode average Qualitative variation Ordinal Median average Interquartile range Interval Mean average Deviation Ratio Geometric or harmonic mean Studentized range

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## The importance of the four levels of measurement

The importance of levels of measurement as a classification system for variables in data sets comes down to how different sets of data are comparable with one another.

Note:

Not all statistical methods can be used with all variables.5

For example, because a ratio level of measurement contains a true zero, it is possible to say whether one variable is three or four times the quantity of another.

Example:

Consider the Kelvin temperature scale which falls into this category.

In it, absolute zero is the true zero needed to fall into this category. Therefore, 373 K, the boiling point of water, can be said to be 1.366 times higher than the freezing point of water – 273 K.

By contrast, the boiling point of water in °C cannot be said to be 100 times higher than water’s freezing point because the use of zero on this scale is arbitrary and not a true zero.

Overall, the four levels of measurement in common use offer a chance to introduce mathematical operations in the correct way, thereby providing insights into more advanced statistical operations.

 Level of measurement Mathematical operand likely to be used Statistical operation Nominal  or  Data aggregation, grouping Ordinal ≤ or ≥ Sorting, categorizing Interval + or - Measurement, comparison to a standard Ratio × or ÷ Measurement, comparison to a standard

## FAQs

#### What are the four levels of measurement?

The four levels of measurement in order are:

• nominal
• ordinal
• interval
• ratio

Although these are the four widely adopted levels of measurement, some academics advocate for and use other classification systems.

#### What is the law of comparative judgment in levels of measurement?

This is a system for judging the interval type of measurement through pairwise comparisons developed by LL Thurstone. It is usually used in analytic hierarchy processes.

#### Why use levels of measurement?

We use levels of measurement to decide the best way to interpret data.

Selecting the most appropriate level helps to produce an analysis that can be peer-reviewed and understood more easily within a pre-existing academic framework.

#### What is a nominal measurement in sociology?

Levels of measurement that can be classified as nominal in the field of sociology include how people might choose to identify or characterize themselves.

Examples of nominal levels of measurement in sociology include:

• social class
• racial identity
• gender
• etc.

## Sources

1 Harvard University. “S. S. Stevens (1906 – 1973).” Accessed March 13, 2023. https://psychology.fas.harvard.edu/people/s-s-stevens.

2 Bose, Bonani. “A Definitive Approach To The Levels Of Measurement.” Digital Vidya. Accessed March 13, 2023. https://www.digitalvidya.com/blog/levels-of-measurement/.

3 Statista. “Definition Level of measurement.” Accessed March 13, 2023. https://www.statista.com/statistics-glossary/definition/386/level_of_measurement/.

4 Laerd Statistics. “Descriptive and Inferential Statistics.” Accessed March 13, 2023. https://statistics.laerd.com/statistical-guides/descriptive-inferential-statistics.php.

5 Buffalo State University. “Levels of Measurement: Overview.” Accessed March 13, 2023. https://library.buffalostate.edu/measurements/overview.

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