Ordinal Data

Ordinal Data Definition:

Ordinal data is a statistical type of quantitative data in which variables exist in naturally occurring ordered categories. The distance between two categories is not established using ordinal data.

In statistics, a group of ordinal numbers indicates ordinal data and a group of ordinal data are represented using an ordinal scale. The main difference between nominal and ordinal data is that ordinal has an order of categories while nominal doesn’t.

Learn more: Nominal vs Ordinal

Likert Scale is a popular ordinal data example. For a question such as: “Please express the importance pricing has for you to purchase a product.”, a Likert Scale will have the following options which are coded to 1,2,3,4 and 5 (numbers). 1 is lesser than 2, which is lesser than 3, which is lesser than 4, which in turn is lesser than 5.  

Very Important Important Neutral Unimportant Very Unimportant
1 2 3 4 5

Ordinal data is thus a collection of ordinal variables, i.e., if you have variables in a particular order – “low, medium, high”, they can be represented as ordinal data. There are two important factors to consider for ordinal data –

  • There are multiple terms that represent “order” such as “High, Higher, Highest” or “Satisfied, Dissatisfied, Extremely Dissatisfied”.
  • The difference between variables is not uniform.

Learn more: Types of Measurement Variables

Ordinal Data Characteristics:

For a question such as the following, here are five ordinal data characteristics:

  • Which of the following categories best describes your last purchasing experiences with a product/service?
    • Very Pleasant
    • Somewhat Pleasant
    • Neutral
    • Somewhat Unpleasant
    • Very Unpleasant
  1. Establish a relative rank: In the above-mentioned example,  Somewhat pleasant is definitely worse than very pleasant or very unpleasant is worse than somewhat unpleasant. There clearly is a rank within the options – which is a sign of ordinal data.
  2. Value of interval is unknown: The variation between very pleasant and somewhat pleasant need not be the same as the difference between somewhat unpleasant and very unpleasant. This interval can’t be concluded using the ordinal scale.
  3. Measure non-numeric traits: In the given example, all the answer options are non-numeric and similarly ordinal data can be used to capture feelings such as satisfaction, happiness, frequency etc.
  4. Add-on to nominal data: Nominal data is “labeled” data. Ordinal data is labeled data in a specific order. In the above mention sample, there is a notable order in the options which makes it a classic case of ordinal data.
  5. Ordinal data has a median: Median is the value in the middle but not the middle value of a scale and can be calculated with data which has an innate order.

Ordinal Data Analysis:

  • Easy methods of Ordinal Data analysis:

Ordinal data is presented in a tabular format which makes analysis easier for the researcher. Mosaic plots are also used to establish the relationship between nominal and ordinal data.

For instance, if an organization intends to analyze the number of employees in each hierarchy to make a systematic hiring process for the upcoming year – they can put this data in an ordered tabular format. HR executives will find this data extremely easy to refer to and analyze for any future updates.   

  • Mann-Whitney U test:

To compare two ordinal data groups, the Mann-Whitney U test should be used. – This test allows a researcher to conclude that a variable from one sample is greater or lesser than another variable randomly selected from another sample.

For example, a psychological researcher can understand various existing behavior patterns so that an analysis of two different medicines can be observed and evaluated.

  • Kruskal–Wallis H test:

To compare more than two ordinal groups, Kruskal–Wallis H test should be used – In this test, there is no assumption that the data is coming from a particular source. This test concludes whether the median of two or more groups is varied. It will show the difference between more than two ordinal data groups.

For example, if a researcher intends to evaluate the impact of stress at work on the quality of work – the independent variable will be stress at work which ideally will have three stages: no stress, too much stress and handleable stress and quality of work will vary from poor to excellent.

Ordinal Data Examples:

  • In a school with 3000 students, there are various categories – freshmen, sophomores, juniors, seniors. After the term begins, this is the count of each category :
    • 1000 – Freshmen
    • 800 – Sophomores
    • 750 – Juniors
    • 450 – Seniors
  • An organization conducts a quarterly employee satisfaction survey which primarily highlights this question: “How happy are you with your manager and peers?”
    • Extremely Happy – 1
    • Happy – 2
    • Neural – 3
    • Unhappy – 4
    • Extremely Unhappy – 5
  • According to your preferences, please rate these 5 best-selling books:
    • Fire and Fury – 1
    • A Higher Loyalty: Truth, Lies, and Leadership – 2
    • The Woman in the Window – 3
    • The Great Alone – 4
    • The Subtle Art of Not Giving a F*ck: A Counterintuitive Approach to Living a Good Life – 5