Understanding and Using Ordinal Data

Introduction

This article explores ordinal data, a type of data with values that have a meaningful order but unknown magnitude between consecutive values. It covers examples such as drink sizes and professional ranks, applications in subjective evaluations like customer satisfaction surveys, appropriate statistical measures, and the qualitative nature of ordinal data. Understanding this data is crucial for accurate data interpretation and analysis.

Overview

• Define and identify ordinal data and distinguish it from other types of data.
• Provide examples of ordinal data in everyday contexts, such as drink sizes and professional ranks.
• Understand how ordinal data is used in subjective evaluations and surveys.
• Know the appropriate statistical measures (mode and median) for analyzing this data.

Ordinal Data

Ordinal data is data with possible values ​​that have a meaningful order or ordering between them, but the magnitude between consecutive values ​​is unknown. It is one type of measurement level.

Ordered Categories:

• Relative rankings
• Unknown distance between rankings
• Zero is arbitrary

Example of Ordinal data

Assume that the size of the drink corresponds to the size of the drinks available at a fast food restaurant. This data has three possible values: small, medium, and large. The values ​​have a meaningful sequence (corresponding to increasing drink size); however, we cannot tell from the values ​​how much larger, say, a medium is compared to a large. Other examples of ordinal data include grades (eg A, B, C, D, and F) and professional ranks. Professional ranks may be listed in sequential order: for example, assistant, assistant, and full for professors, and private, private first class, specialist, corporal, and sergeant for army ranks.

Examples:

• Likert scales
• Socioeconomic status
  • x 1 = Low
  • x 2 = Middle
  • × 3 = High
• Size
  • 1 = Small
  • 2 = Medium
  • 3 = Large
• Size, ranking of favorite sports, class rankings, wellness rankings

Application

Ordinal data is useful for recording subjective evaluations of qualities that cannot be measured objectively. Thus, this data are often used in evaluation surveys. For example, in one survey, participants were asked to rate the satisfaction of their customers. Customer satisfaction had the following ordinal categories:

• 0: very dissatisfied
• 1: somewhat dissatisfied
• 2: neutral
• 3: satisfied
• 4: very satisfied

Researchers can also obtain this data by discretizing numerical quantities, dividing the range of values into a finite number of ordered categories.

Customer Satisfaction

• Are you “very satisfied,” “satisfied,”
• “neither satisfied nor dissatisfied,”
• “dissatisfied,” or
• “very dissatisfied.”

Movie Ratings

Statistical Measures for Ordinal Data

Ordinal data can be analyzed using several statistical measures that offer insights into central tendency and distribution. The mode identifies the most frequent value, while the median divides data equally. The range spans from the smallest to largest values, showing data variability. The Interquartile Range (IQR) between Q3 and Q1 depicts middle 50% values. Frequency distribution and percentiles divide data into 100 parts, showing distribution, while cumulative frequency shows totals in a range

Qualitative Nature

It is important to note that nominal, binary and ordinal data are qualitative. They describe a feature of an object without stating the actual size or quantity. The values ​​of such qualitative data are typically words representing categories. When integers are used, they represent computer codes for categories, as opposed to measurable quantities (eg, 0 for a small drink, 1 for a medium, and 2 for a large).

In the next subsection, we will look at numerical attributes that provide a quantitative measurement of an object.

Conclusion

Ordinal attributes play a key role in various fields by providing a way to categorize data in a meaningful order. Despite the lack of precise measurement between successive values, these attributes are necessary to capture subjective evaluations and order categories in a logical sequence. They are particularly valuable in surveys, assessments and professional hierarchies where qualitative judgment is required. An understanding of appropriate statistical measures such as mode and median further enhances the usefulness of ordinal attributes in data analysis. Recognizing the difference between qualitative ordinal attributes and quantitative numerical attributes ensures accurate interpretation and use of data in research and decision-making processes.

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Janvi Kumari

Hi, I am Janvi, a passionate data science enthusiast currently working at Analytics Vidhya. My journey into the world of data began with a deep curiosity about how we can extract meaningful insights from complex datasets.