Ordinal Data

March 19, 2021

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There are four primary scales of measurement used for classification purposes:

Nominal, where numbers identify and classify objects.
Ordinal, where numbers indicate the relative positions of objects, however not the magnitude of difference between them.
Interval, where differences between objects can be compared, and zero point is arbitrary.
Ratio, where the zero point is fixed and ratio of scale values can be computed.

In this article we will specifically be delving into ‘ordinal data’ and its examples.

What is Ordinal Data?

The word “ordinal” roots from the late latin word “ordinalis” meaning ‘relating to order in a series’. Therefore, as the name suggests, ordinal data is data/information that has a set order or scale to it. Being widely used in market research, it is a categorical & statistical data type in which variables are ordered without defined distances between the known categories.

Ordinal data is represented using “ordinal scales”. Ordinal scales allow you to determine whether an object has less or more of a certain characteristic than another. However, it is important to note that ordinal scales don’t outline how much less or more this difference is.

Two important factors that must be considered in regard to ordinal data:

The difference between variables on the ordinal scale is not always the same.
Multiple terms may be used to represent “order”.

To better understand these factors, let’s look at a popular form of ordinal data; the likert scale. This scale is used in market research surveys or questionnaires and is usually a five point scale where the respondents can choose from ‘strongly disagree’, ‘disagree’, ‘neutral’, ‘agree’, and ‘strongly agree’. This scale has a clear order. However, there is no way of identifying how different variables on this scale are from each other. The difference between “strongly agree” and “agree” may be more or less than the difference between “disagree” and “strongly disagree”.

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Characteristics of Ordinal data

Let’s look at the following example to better understand the characteristics of ordinal data:

Choose a response based on how you feel about the following statement.

I enjoy the work I do.

Strongly agree
Agree
Neutral
Disagree
Strongly disagree

Has a median: Ordinal data scales have a median value. This isn’t necessarily the middle value on the scale and it can be calculated using data that has an innate order.
No standardisation of interval scale: A standard interval cannot be defined using an ordinal scale. In the example above, the difference between ‘strongly agree’ and ‘agree’ may not be the same as the difference between ‘neutral’ and ‘disagree’.
Extension of Nominal Data: Ordinal data is considered an extension of nominal data. This is because nominal data is “named” data, and ordinal data is also “named” data but with a rank or specific order to it as well.
Can measure non-numeric/qualitative traits: As reflected in the example above where the questions aims to get a grasp of a respondent’s satisfaction at work, ordinal data can be used to measure feelings and other qualitative variables required for market research.
Establishes a relative rank: In the example above, it is established that “Strongly agree” means someone agrees more with the statement than they would have if they chose “agree”. This reflects the presence of relative ranks.
Can measure numeric values: Some ordinal scales may be numeric. For example, if you had to rate your satisfaction at work from a scale of 1-10. Even scales that aren’t numeric can be given ranks if it is an ordinal scale. However, numeric operations cannot be performed on these values.

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Analysis of Ordinal data

Wilcox rank-sum test

Wilcox rank-sum test, also known as Mann-Whitney U test, is a qualitative statistical test used to investigate 2 groups of independent samples. It allows the researcher to compare two samples from two different ordinal data groups. It can identify whether they are greater or lesser than each other.
Kruskal-Wallis H test

This test is used to define whether the median of two or more groups is varied, and can show the difference between two data groups on an ordinal scale.

Examples of Ordinal Data

A researcher conducts a study on social attitudes toward Marijuana and the following is a question in a survey for the research:

Nominal variables cannot be ordered whereas ordinal variables can.
Quantitative values cannot be associated with nominal variables but can be associated with ordinal variables. However the numbers associated with ordinal variables cannot be used to conduct any sort of arithmetic evaluation.