What is Ordinal Data? Definition, Examples, Variables & Analysis

What Is Ordinal Data?

Ordinal data is a kind of qualitative data that groups variables into ordered categories, which have a natural order or rank based on some hierarchal scale, like from high to low. But there is a lack of distinctly defined intervals between the categories. In terms of levels of measurement, ordinal data ranks second in complexity after nominal data. 

We use ordinal data to observe customer feedback, satisfaction, economic status, education level, etc. Such data only shows the sequences and cannot be used for statistical analysis. We cannot perform arithmetical tasks on ordinal data.   

Ordinal Data Characteristics

• Ordinal data are non-numeric or categorical but may use numerical figures as categorizing labels. 
• Ordinal data are always ranked in some natural order or hierarchy. So, they are termed ordinal.
• Ordinal data is labeled data in a specific order. So, it can be described as an add-on to nominal data. 
• Ordinal data is always ordered, but the values are not evenly distributed. The differences between the intervals are uneven or unknown. 
• Ordinal data can be used to calculate summary statistics, e.g., frequency distribution, median, and mode, range of variables. 
• Ordinal data has a median. 

Ordinal Variables

Ordinal variables are categorical variables with ordered possible values. They can be considered as “in-between” categorical and quantitative variables.  

Ordinal variables can be classified as:

Matched Category 

In this category, each member of a data sample is matched with similar members of all other samples in terms of all other variables apart from the one considered. This helps get a better estimation of differences. Elimination of other variables prevents their influence on the results of the investigation being done. 

There are two types of tests done on the matched category of variables –

• Wilcoxon signed-rank test
• Friedman 2-way ANOVA

Unmatched Category

In this category, unmatched or independent samples are randomly selected with variables independent of the values of other variables. 

The tests done on the unmatched category of variables are – 

• Wilcoxon rank-sum test or Mann-Whitney U test
• Kruskal-Wallis 1-way test

Ordinal Data Examples

Ordinal data often include ratings about opinions or feelings or demographic factors like social status or income that are categorized into levels.

Interval Scale

An Interval Scale is a kind of ordinal scale where each response is in the form of an interval on its own. 

Examples:

1. Rank economic status according non-equally distributed to Income level range:

• Poor or Low Income ($10K-$20K) 
• Middle income ($20K-$35K)
• Wealthy ($35K-$100K)

2. Rate education level according to:

• Elementary
• High School
• College
• Graduate
• Post-graduate

Likert Scale

A Likert Scale refers to a point scale that researchers use to take surveys and get people’s opinions on a subject.  

Examples:

1. An organization asks employees to rate how happy they are with their manager and peers according to the following scale:

• Extremely Happy – 1
• Happy – 2
• Neural – 3
• Unhappy – 4
• Extremely Unhappy – 5 

2. Company asking customers for Feedback, experience, or satisfaction on the scale

• Very satisfied
• Satisfied
• Neutral
• Dissatisfied
• Very dissatisfied

How to Analyze Ordinal Data?

The level of measurement you use on ordinal data decides the kind of analysis you can perform on the data. Ordinal data can be analyzed using Descriptive Statistics and Inferential Statistics.

Descriptive Statistics allows you to summarize a dataset's characteristics, while Inferential Statistics helps make predictions based on current data. 

The following Descriptive Statistics can be obtained using ordinal data:

• Frequency Distribution – Describes, in numbers or percentages, how your ordinal data are distributed. For example, you can summarize grades received by students using a pivot table or frequency table, where values are represented as a percentage or count. The table enables you to see how the values are distributed. 
• Another way of overviewing frequency distribution is by visualizing the data through a bar graph. The order of categories is important while displaying ordinal data. 
• Measures of central tendency: Mode and/or median – the central tendency of a dataset is where most of the values lie. The mean, median (the central value) and mode (the value that is most often repeated) are the most common measures of central tendency. However, since ordinal data is not numeric, identifying the mean through mathematical operations cannot be performed with ordinal data.     

The mode can be easily identified from the frequency table or bar graph. 

The median value is: 

The value in the middle of the dataset for an odd-numbered set

The mean of the two values in the middle of an even-numbered dataset

Measures of variability: Range – variability can be assessed by finding a dataset's minimum, maximum, and range. Numeric codes need to be used to calculate this. The range is useful as it indicates how spread out the values in a dataset is. 

Inferential Statistics

Inferential Statistics help infer broader insights about your data. Statistical tests work by testing hypotheses and drawing conclusions based on knowledge. These tests can be parametric or non-parametric. Only Non- Parametric tests can be used with ordinal data since the data is qualitative. 

Some Non-parametric tests that can be used for ordinal data are:

• Mood’s median test – to compare the medians of two or more samples and determine their differences.
• The Mann-Whitney U test – compares whether two independent samples belong to the same population or if observations in one sample group tend to be larger than in another. 
• Wilcoxon signed-rank test – to compare how and by how much the distribution of scores differ in two dependent samples of data or repeated measures of the same sample.
• The Kruskal-Wallis H test – compares mean rankings of scores in three or more independent data samples. The test helps determine if the samples originate from a single distribution.  
• Spearman’s rank correlation coefficient – to explore correlations between two ordinal variables. This test measures the statistical dependence between the rankings of the variables.

Nominal vs. Ordinal Data

Nominal data is another qualitative data type used to label variables without a specific order or quantitative value. 

The main differences between Nominal Data and Ordinal Data are:

• While Nominal Data is classified without any intrinsic ordering or rank, Ordinal Data has some predetermined or natural order. 
• Nominal data is qualitative or categorical data, while Ordinal data is considered “in-between” qualitative and quantitative data.
• Nominal data do not provide any quantitative value, and you cannot perform numeric operations with them or compare them with one another. However, Ordinal data provide sequence, and it is possible to assign numbers to the data. No numeric operations can be performed. But ordinal data makes it possible to compare one item with another in terms of ranking.  
• Example of Nominal Data – Eye color, Gender; Example of Ordinal data – Customer Feedback, Economic Status

Frequently Asked Questions

1. What is ordinal data?

Ordinal data is a kind of qualitative data that groups variables into ordered categories. The categories have a natural order or rank based on some hierarchal scale, like from high to low. But there is no clearly defined interval between the categories.

2. What are the four levels of measurement?

Levels of measurement indicate how precisely variables have been recorded. The four levels of measurement are:

• Nominal: the simplest data type where data can only be categorized.
• Ordinal: the data can be categorized while introducing an order or ranking.
• Interval: the data can be categorized and ranked, in addition to being spaced at even intervals.
• Ratio: the most complex level of measurement. Here data can be categorized, ranked, and evenly spaced. It also has a true zero.

3. What’s the difference between nominal and ordinal data?

Nominal and ordinal are two levels of measurement. While Nominal Data can only be classified without any intrinsic ordering or rank, Ordinal Data can be classified and has some kind of predetermined or natural order. 

4. Are ordinal variables categorical or quantitative?

Ordinal variables are categorical variables that contain categorical or non-numeric data representing groupings. 

5. Are Likert scales ordinal or interval scales?

A Likert Scale refers to a point scale that researchers use to take surveys and get people’s opinions on a specific subject. Individual Likert scale score is generally considered ordinal data since the values have clear rank or order but do not have an evenly spaced distribution. 

However, overall Likert scale scores are often considered interval data possessing directionality and even spacing. 

Conclusion

What we discussed here scratches the tip of the iceberg with ordinal data, examples, variables, and analysis. If you’re interested in diving deep into these topics or looking to build a career in the lucrative data science field, we recommend exploring our top-ranked courses, like Caltech Post Graduate Program In Data Science.