In the sphere of statistics, the comprehension of levels of measurement is essential for conducting proper data analysis and assessment. These levels are nominal level, ordinal level, interval level, and ratio level. Depending on their type and specific characteristics, they classify different values of data. It is influential for researchers to determine the appropriate level of measurement for their study to employ relevant analytical methods to draw valid conclusions.
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Levels of Measurement – In a Nutshell
This article delves into the four different types of levels of measurements that are primarily used in statistics:
- Nominal
- Ordinal
- Interval
- Ratio
Each classification – or level – helps to make it easier to understand the types 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 accordingly, ensuring accurate conclusions and results.
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.
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.
The nominal level of measurement is regarded as the lowest on the scale. In other words, nominal data variables can only be categorized.
Examples
- Someone’s gender
- Their place of birth
- The country they reside in
The ordinal level of measurement is regarded as the second-lowest on the scale. In other words, ordinal data variables can be ranked as well as categorized.
Examples
- 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
The interval level of measurement is regarded as the second-highest on the scale. I.e., interval data variables can be evenly spaced as well as ranked and categorized.
Examples
- The temperature in °C, recorded at hourly intervals during the day
- Scores a group of individuals achieves following an IQ or personality test
The ratio level of measurement is regarded as the highest on the scale. I.e., ratio data variables can be evenly spaced as well as ranked and categorized just like the interval level.
Examples
- 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.
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 | Harmonic or Geometric mean | Studentized range |
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.
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.
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
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.
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.
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.
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.