Level of Measurement

What are the levels of measurement?

Level of measurement refers to how we classify and organize data. It helps us understand what kind of information the data provides and determines the types of calculations and analyses we can perform.

There are three main levels: nominal, ordinal, and metric. The metric level of measurement can further be divided into interval and ratio. In a nutshell: nominal values can be distinguished, ordinal values can also be ranked, and metric values have meaningful distances between them.

Levels of measurement therefore describe the ways variables can be categorized or quantified. Each variable in a data set can usually be classified using one of these levels, although the appropriate classification can depend on how the variable was defined and measured.

In practice, interval and ratio data are often used to perform the same analyses. Therefore, the term 'metric level' is used to combine these two levels.

Why You Need Levels of Measurement

The level of measurement is crucial in statistics for several key reasons. It tells us how our data can be collected, analyzed, and interpreted.

Different levels of measurement support different statistical analyses. For instance, means and standard deviations are generally suitable for metric data. They are sometimes used for ordinal data, such as a scale formed from several questionnaire items, but this requires a clear justification and careful interpretation. Means and standard deviations are not meaningful for nominal categories.

The level of measurement also helps us choose suitable hypothesis tests and data visualizations.

Nominal Variables

The nominal measurement scale distinguishes categories but does not place them in a meaningful order. If a nominal variable has only two categories, such as a yes/no response, we also speak of dichotomous or binary variables.

• Only relations "equal" and "unequal" are possible.
• No logical ranking of categories.
• The order of the answer categories is interchangeable.
• Nominal characteristics with only two categories are also called "binary" or "dichotomous".

Ordinal Variables

The ordinal level of measurement distinguishes categories and places them in a meaningful order. It is therefore also called a ranking scale. The distances between categories are not known to be equal, so numerical differences cannot be interpreted as fixed amounts. A classic example is school grades: a ranking can be formed, but it cannot be assumed that the distance between A and B is the same as the distance between B and C.

• "Equal" and "unequal", as well as "greater" and "smaller", can be determined.
• There is a logical hierarchy of categories.
• The distances between categories are not known to be equal and cannot be interpreted as fixed amounts.

Categorical Variables

Variables that have a nominal scale or an ordinal scale are also called categorical variables. In other words, categorical is an umbrella term for variables scaled nominally and ordinally.

In a particular data set, categorical variables usually have a limited set of observed categories, for example countries such as "Germany" and "Austria." The possible categories do not have to be inherently finite. Categories may have an order (ordinal) or no meaningful order (nominal).

Metric Variables

Metric variables are quantitative variables for which differences between values are meaningful. Their values can be compared and sorted, and distances between them can be calculated. Examples include weight and age.

• Includes interval and ratio scales.
• Creation of rankings possible.
• "Equal" and "unequal", as well as "greater" and "smaller", can also be determined.
• Differences are meaningful on an interval scale. Differences and ratios are meaningful on a ratio scale.

Ratio Scale and Interval Scale

The metric level of measurement can be further divided into interval and ratio scales. A ratio scale has equal intervals and a meaningful zero that represents the absence of the measured quantity. This makes statements such as "one value is twice another" meaningful. An interval scale also has equal intervals, but its zero point is arbitrary, so ratios are not meaningful.

Temperature measured in kelvins is a ratio-scale variable because 0 K is absolute zero. Temperature measured in degrees Celsius is an interval-scale variable because 0 °C is an arbitrary reference point; absolute zero is -273.15 °C.

Level of Measurement Examples