# Levels of Measurement: Nominal, Ordinal, Interval and Ratio Variables

What are the four levels of measurement with examples? The direct answer is Nominal, ordinal, interval, and ratio variables. On this webpage, you will learn about the levels of measurement or scales of measurement.  Levels of measurement, also called scales of measurement, tell you exactly how a data variable has been recorded. A data variable can take any range of values across your data set, ranging from qualitative values (e.g., names, eye color, level of education, etc.) to quantitative values (e.g., height, age, etc.) and everything in between.

Understanding how a data variable has been recorded before conducting any data analysis is critical. Therefore, understanding the level of measurement of specific data variables in your data set helps you know what you can do to analyze the data, as some levels of measurement might limit your options significantly.

There is also a hierarchy in the precision and complexity of the scales of measurement, from nominal data, the lowest, to ratio data, the highest. However, these levels of measurement are also cumulative, meaning that higher levels can take on the properties of lower levels and then add on new features. Confused? Don’t be; let’s delve deeper into each of these scales of measurement, and hopefully, it will all make sense.

## Nominal Variables

Nominal variables are categorical variables that allow you to group data into mutually exclusive categories, but there is no natural order. Data variables like gender, ethnicity, eye color, car brands, marital status, and place of birth are nominal variables because while you can group data into either of these categories, there is no natural order to them. For example, you can label the gender variable as 1 for male and 2 for female, or vice versa, but these numbers do not imply any ranking between the genders.

## Ordinal Variables

Ordinal variables, like nominal variables, are also categorical variables that allow you to group data into mutually exclusive categories. However, unlike nominal variables, there is a natural order in these categories, despite not telling you anything about the intervals between the rankings. Data variables like education level, customer satisfaction, language fluency, or other Likert-type questions are ordinal because they have a meaningful order. However, the labels do not indicate how far apart the categories are.

For example, consider the language fluency variable, with the following categories: beginner, intermediate, and fluent. While there is a meaningful order of language expertise from beginner to intermediate and finally to fluent, these categories do not indicate how far apart one category is from the other. Thus, we do not know if the difference between beginner and intermediate is similar to the difference between intermediate and fluent.

## Interval Variables

Interval variables are also categorical, with a meaningful order and equal distances between adjacent values but no true zero point. Therefore, the difference between interval variables and ordinal or nominal variables is that they have a standardized unit of measurement or a meaningful numerical difference between the values. Interval variables include temperature, standardized test scores, time scales, or psychological inventories like IQ scores.

Take the temperature variable using degrees Celsius. This is an interval variable because the difference between 21 and 22 degrees is the same as between 200 and 201 degrees. However, zero degrees does not mean the absence of heat.

## Ratio Variables

Finally, ratio variables are categorical variables with a natural order between categories, equal distances between adjacent values, and a true zero point. In this case, a true zero means the complete absence of the variable of interest. Therefore, ratio variables cannot take negative values. Ratio variables include temperature in Kelvin, age, weight, height, and so forth.

For example, using a temperature Kelvin scale, we cannot have negative degrees of temperature because 0 degrees Kelvin means an absolute lack of thermal energy.

## Why Levels of Measurement are Important in Data Analysis

The scales of measurement play a key role in the descriptive analysis that you can conduct on your data. Descriptive statistics allow you to summarize and organize your data, while also better understanding the characteristics and patterns of the data set. There are three primary types of descriptive statistics: measures of central tendency, measures of variability, and frequency distributions.

The scales of measurement determine the methods you can implement based on the mathematical operations appropriate for each level. The appropriate methods, like the scales of measurement themselves, are cumulative, meaning that you can apply all the mathematical methods you used in lower levels at higher levels of measurement, plus more.

The following table clearly outlines the mathematical operations and measures of central tendency and variability that you can use for each scale of measurement. Understandably, some of these methods, like geometric mean and relative standard deviation, are rarely utilized in statistical operations, but it is useful to see where they can be used.

## Levels of Measurement in Statistical Analysis Example

 Scale of measurement Mathematical operations Measures of central tendency Measures of variability Nominal Equality (=, ≠) Mode None Ordinal Equality (=, ≠) Comparison (>, <) Mode Median Range Interquartile Range Interval Equality (=, ≠) Comparison (>, <) Addition, Subtraction (+, -) Mode Median Arithmetic Mean Range Interquartile Range Standard Deviation Variance Ratio Equality (=, ≠) Comparison (>, <) Addition, Subtraction (+, -) Multiplication, Division (×, ÷) Mode Median Arithmetic Mean Geometric Mean Range Interquartile Range Standard Deviation Variance Relative Standard Deviation

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