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Ordinal data classification is an integral step toward the proper collection and analysis of data. Therefore, in order to classify data correctly, we need to first understand what data itself is.

Data is a collection of facts or information from which conclusions may be drawn. They can exist in various forms – as numbers or text on pieces of paper, as bits and bytes stored in electronic memory, or as facts stored in a person’s mind.

When dealing with data, they are sometimes classified as nominal or ordinal. Data is classified as either nominal or ordinal when dealing with categorical variables – non-numerical data variables, which can be a string of text or date.

## Definition of Ordinal Data

Ordinal data is a kind of categorical data with a set order or scale to it. For example, ordinal data is said to have been collected when a responder inputs his/her financial happiness level on a scale of 1-10. In ordinal data, there is no standard scale on which the difference in each score is measured.

Considering the example highlighted above, let us assume that 50 people earning between \$1000 to \$10000 monthly were asked to rate their level of financial happiness.

An undergraduate earning \$2000 monthly may be on an 8/10 scale, while a father of 3 earning \$5000 rates 3/10. This is to show that the scale is usually influenced by personal factors and not due to a set rule.

Read Also: What is Nominal Data? Examples, Category Variables & Analysis

## Ordinal Data Examples

Examples of ordinal data include the Likert scale; used by researchers to scale responses in surveys and interval scale; where each response is from an interval of its own. Unlike nominal data, ordinal data examples are useful in giving order to numerical data.

• Likert Scale:

A Likert scale is a point scale used by researchers to take surveys and get people’s opinions on a subject matter. It is usually a 5 or 7-point scale with options that range from one extreme to another. Consider this example:

How satisfied are you with our meal tonight?

1. Very satisfied
2. Satisfied
3. Indifferent
4. Dissatisfied
5. Very dissatisfied

This is a 5-point Likert scale. Like in this example, each response in a 5-point Likert scale is assigned to a numeric value from 1-5.

Read Also: 7 Types of Data Measurement Scales in Research

• Interval Scale

An interval scale is a type of ordinal scale whereby each response is an interval on its own. Examples of interval scales include; the classification of people into teenagers, youths, middle-aged, etc. done according to their age group.

In which category do you fall?

• Child – 0 to 12 years
• Teenager – 13 to 19 years
• Youth – 20 to 35 years
• Middle age – 36 to 58 years
• Old – 59 years and above

Example 2: In a school, students are graded as either A, B, C, D, E, or F according to their score. Students that score 70 and above are graded A, 60-69 are graded B, and so on.

1. 70 and above
2. 60-69
3. 50-59
4. 40-49
5. 35-40
6. 34 and below.

## Categories of Ordinal Variables

Ordinal variables can be classified into 2 main categories, namely; the matched and unmatched categories. This ordinal variable classification is based on the concept of matching – pairing up data variables with similar characteristics.

According to Wikipedia, matching is a statistical technique that is used to evaluate the effect of a treatment by comparing the treated and non-treated units in an observational study or quasi-experiment (i.e. when the treatment is not randomly assigned).

### The Matched Category

In the matched category, each member of a data sample is paired with similar members of every other sample with respect to all other variables, aside from the one under consideration. This is done in order to obtain a better estimation of differences.

By eliminating other variables, we are able to prevent them from influencing the results of our current investigation. For example, when investigating the cause of skin cancer, it is better to match people of the same race together because of melanin deficiency (a condition common to white people) is a known cause.

#### Tests

There are 2 different types of tests done on the Matched category, depending on the number of sample groups that are being investigated. Namely; the Wilcoxon signed-rank test and Friedman 2-way Anova

• Wilcoxon signed-rank test: This is a qualitative statistical test used to compare the 2 groups of matched samples to assess their differences.
• Friedman 2-way ANOVA: This is a non-parametric way of finding differences in matched sets of 3 or more groups. Developed by Milton Friedman, this test procedure involves ranking rows together, then considering the values of each rank by columns.

### The Unmatched Category

Unmatched samples, also known as independent samples are randomly selected samples with variables that do not depend on the values of other ordinal variables. Most researchers base their analysis on the assumption that the samples are independent, except in a few cases.

For example, suppose examiners want to compare the efficiency of 2 test marking software. They take random samples of 10 students’ answer scripts and send them to the two  (2) software for marking. It doesn’t matter whether the answers ticked by these students are similar or not.

#### Tests

• Wilcoxon rank-sum test

The Wilcoxon rank-sum test is also known as the Mann-Whitney U test. It is a non-parametric test used to investigate 2 groups of independent samples. This test is usually used to test whether the samples belong to the same population. A similar qualitative test used on matched samples is the Wilcoxon signed-rank test.

• Kruskal-Wallis 1-way test

This is a non-parametric test for investigating whether 3 or more samples belong to the same population. Named after William Kruskal and W. Allen Wallis, this test concludes whether the median of two or more groups is varied.

Characteristics of Ordinal Data

• Extension of nominal data

Ordinal data is built on the existing nominal data. Nominal data is known as “named” data, while ordinal data is “named” data with a specific order or rank to it. Let us consider the ordinal data example given below:

Which of the following best describes your current level of financial happiness?

• Very happy
• Happy
• Neutral
• Unhappy
• Very unhappy

The options in this question are qualitative, with a rank or order to it. The rank, in this case, is a sign of ordinal data.

• No standardized interval scale

The difference in variation between “Very happy” and “happy” does not necessarily have to be the same as the one between “happy” and “neutral”. There is no standardized interval scale of measurement for each variable.

In fact, the difference in variation can’t be concluded using the ordinal scale. This scale is dependent on factors that are unique for each respondent.

• Establish a relative rank

In the example mentioned above, ”very happy” is definitely better than “unhappy” and “neutral” is worse than “happy”. Unlike the interval scale, there is an established rank of order in this case.

This rank is used to group respondents into different levels of happiness.

• Measure qualitative traits

The ordinal scale has the ability to measure qualitative traits. The measurement scale, in this case, is not necessarily numbers, but adverbs of degree like very, highly, etc.

In the given example, all the answer options are qualitative with “very” being the adverb of degree used as a scale of measurement.

• Measure numeric values

Ordinal data can also be quantitative or numeric. When asked to rate your level of financial happiness, for example, the values are numeric. However, numerical operations (addition, subtraction, multiplication, etc.) cannot be performed on them.

• Has a median

Unlike nominal data where only the mode can be calculated, ordinal data has a median. The median is the value in the middle but not the middle value of a scale and can be calculated with data that has an innate order. Consider the ordinal variable example below.

Rate your knowledge of Excel according to the following scale.

• Intermediate
• Basic
• Novice
• Zero

In this example, the middle value is “Basic” while the value in the middle is “intermediate”.

• Has an order: Ordinal data has a specific rank or order, which may either be ascending or descending.

## Ordinal Data Analysis and Interpretation

Ordinal data analysis is quite different from nominal data analysis, even though they are both qualitative variables. It incorporates the natural ordering of the variables in order to avoid loss of power. Ordinal variables differ from other qualitative variables because parametric analysis median and mode are used for analysis

This is due to the assumption that equal distance between categories does not hold for ordinal data. Therefore, positional measures like the median and percentiles, in addition to descriptive statistics appropriate for nominal data should be used instead.

The use of parametric statistics for ordinal data variables may be permissible in some cases, with methods that are a close substitute to mean and standard deviation. Here are some of the parametric statistical methods used for ordinal analysis.

• Univariate statistics: Used in place of mean and standard deviation, the appropriate univariate statistics for ordinal data include the median, quartiles, percentiles, and quartile deviation.
• Bivariate statistics: Mann-Whitney, Smirnov, runs and signed-rank tests are used in lieu of testing differences in mean with t-test.
• Regression applications: Outcomes are predicted using a variant of ordinal regression, such as ordered probit or ordered logit.
• Linear trends: It is used to find similarities between ordinal data and other variables in contingency tables.
• Classification methods: This method uses matching to categorize data, after which dispersion is measured and minimized in each category to maximize classification results.

## Graphical Techniques To Analyse Ordinal Variables

Ordinal data can also be analyzed graphically with the following techniques.

• Bar chart
• Pie chart
• Tables
• Mosaic plots
• Bump chart

## Uses of Ordinal Data

• Surveys/Questionnaires

Ordinal data is used to carry out surveys or questionnaires due to its “ordered” nature. Statistical analysis is applied to collect responses in order to place respondents into different categories, according to their responses.  The result of this analysis is used to draw inferences and conclusions about the respondents with regard to specific variables. Ordinal data is mostly used for this because of its easy categorization and collation process.

• Research

Researchers use ordinal data to gather useful information about the subject of their research. For example, when medical researchers are investigating the side effects of a medication administered to 30 patients, they will need to collect ordinal data.

After using the medication, each patient may be asked to fill out a form, indicating the degree to which they feel some potential side effects. A sample ordinal data collection scale is illustrated below.

How often do you feel the following?

Very often not often

Nausea                  ¤ ¤ ¤

Dizzy                      ¤ ¤ ¤

Hungry                   ¤ ¤ ¤

• Customer service

Companies use ordinal data to improve their overall customer service. After using their service or buying their product, many companies are known to ask customers to fill out an after-service form, describing their experience.

This will help companies improve their customer service. Consider the example below:

How will you rate our service?

Food                   ¤ ¤ ¤

Waiter                 ¤ ¤ ¤

Waiting time        ¤ ¤ ¤

Environment       ¤ ¤ ¤

• Job applications

During job applications, employers sometimes use a Likert scale to collect information about the level of the applicant’s skill in a field. When an applicant is applying for a social media manager position, for instance, a Likert scale may be used to know how familiar an applicant is with Facebook, Twitter, LinkedIn, etc.

E.g. How familiar are you with the following social networks?

1  2 3  4 5

Facebook        ¤ ¤ ¤ ¤ ¤

Instagram        ¤ ¤ ¤ ¤ ¤

Twitter             ¤ ¤ ¤ ¤ ¤

LinkedIn          ¤ ¤ ¤ ¤ ¤

• Personality tests

This is a common test that is usually administered by employers to their potential employees. This is done so that the employer will know whether the applicant is a good fit for the organization.

Some psychologists also use this to get more information about their patients before treatment. That way, they are able to know which questions to ask, what to say and what not to say.

• The options do not have a standardized interval scale. Therefore, respondents are not able to effectively gauge their options before responding.
• The responses are often so narrow in relation to the question that they create or magnify bias that is not factored into the survey. For example, in the customer service example cited above, a customer might be satisfied with the taste of the meal, but the meat was too tough or the water too cold. In the end, the restaurant will have a report on customer experience, but not be able to differentiate the reason why they chose the response they did.
• It does not allow respondents the opportunity to fully express themselves. They are usually restricted to some predefined options.

## Why Formplus is the Best Tool For Collecting Ordinal Data

• 30+ Field Types
• With a wide range of field types, you can easily collect ordinal data.
• Fields like matrices and scales make it easy to collect any set of ordinal data you need from your respondents.
• Do you need your respondents to give you repeatable data where they specify how many times they want to fill a field?
• You can also use tables if you need to collect ordinal data that is repeatable.

Collect data in remote locations or places without reliable internet connection with Formplus. Offline forms can also act as a backup to the standard online forms, especially in cases where you have unreliable WiFi, such as large conferences and field surveys.

When responders fill a form in the offline mode, responses are synced once there is an internet connection. Using conversational SMS, you can also collect data on any mobile device without an internet connection.

• Share & Export Data in Different Formats

You can store collected data in tabular format or even export it as PDF/CSV. Respondents can also submit their responses as PDFs, Doc attachments, or as images. These responses can also be shared as links through other applications like Gmail, WhatsApp, LinkedIn, etc.

The notification could be set such that, you can choose who on your team should receive these emails if you need to route them directly to the responsible people.

Formplus also allows you to customize the content of the notification message sent to respondents based on what they have filled out in the form.

• Ability to Customise Forms

With Formplus, you can choose how you want your forms to look. You can create an attractive and interactive form that makes your respondents feel encouraged to respond. There are also different choice options for you to choose from.

You have the ability to choose how and when you receive notifications. There is also a customizable feature on the notifications sent to respondents upon completion of the form.

In the event that you are working with a team, you can also add team members to your list of notification recipients.

• Different Storage Options

Formplus allows you to choose how you want to store data. After exporting data in tabular, CSV, or PDF format, you can either save them on your device or upload them to the cloud.

Although Formplus has a cloud platform, you can also upload your data on Dropbox, Google Drive, or Microsoft OneDrive. There are no limitations to the number of files, images, or videos that can be uploaded.

## Conclusion

Ordinal data is designed to infer conclusions, while nominal data is used to describe conclusions. Descriptive conclusions organize measurable facts in a way that they can be summarised.

If a restaurant carries out a customer satisfaction survey by measuring some variables over a scale of 1-5, then the satisfaction level can be stated quantitatively. However, no inference can be drawn about why some customers are satisfied and some are not.

The only inference that can be made is something like, “Most customers are (dis)satisfied”. This is, however, not the case for descriptive conclusions, where one can get enough information on why customers are (dis)satisfied.

Reference

• busayo.longe

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