What is ordinal data? | Examples & Definitions (2023)

Posted on September 18, 2022 byPritha Bhandari.

ordinal datait is sorted into categories within a variable that have a natural sort order. However, the distances between categories are uneven or unknown.

For example, the variable “frequency of physical exercise” can be categorized as follows:

1. never2. Rarely3. Sometimes4. Often5. Always

There is a clear order in these categories, but we cannot say that the difference between "never" and "rarely" is exactly the same as that between "sometimes" and "often". Therefore, this scale is ordinal.

table of contents

  1. measurement levels
  2. Examples of ordinal scales
  3. How to collect ordinal data
  4. How to analyze ordinal data
  5. Common questions

measurement levels

ordinal is the second of 4 hierarchicalmeasurement levels: nominal, ordinal, interval and ratio. Measurement levels indicate how accurately data is recorded.

While nominal and ordinal variables arecategoricalThe range and ratio variables are quantitative.

What is ordinal data? | Examples & Definitions (1)

nominal datait differs from ordinal data in that it cannot be sorted into an order.interval datadiffers from ordinal data because the differences between adjacent scores are equal.

Examples of ordinal scales

In social science research, ordinal variables often include ratings on opinions or perceptions, or demographic factors that are categorized into levels or ranges (such as social status or income).

Variableordinal values
language ability
  • Beginner
  • Intermediary
  • Fluent
level of agreement
  • strongly disagree
  • I disagree
  • I do not agree nor disagree
  • To accept
  • Totally agree
income level
  • Lower Level Income
  • mid-level income
  • top level income

How to collect ordinal data

Ordinal variables are usually evaluated using closed variables.surveyquestions that give participants several possible answers to choose from. They are easy to use and allow you to easily compare data across participants.

To askoptions
How old are you?
  • 0-18
  • 19-34
  • 35-49
  • 50+
what is your education level?
  • Primary school
  • Secondary school
  • Graduation
  • Master's degree
  • Doctor
In the last three months, how many times did you buy groceries online?
  • None
  • 1-4 times
  • 5-9 times
  • 10-14 times
  • 15 or more times

Choice of measurement level

Some types of data can be recorded at more than one level. For example, for the age variable:

(Video) Qualitative Data - Why ? What? || Nominal Data || Ordinal Data || Statistics for Beginners

  • You can collect ordinal data by asking participants to select from four age groups, as in the previous question.
  • you could collectrelationship dataasking participants their exact age.

The more precise level is always preferred for data collection because it allows you to do more mathematical and statistical analysis.

Likert scale data

In the social sciences, ordinal data are often collected usingLikert-type scales. Likert scales are made up of 4 or more Likert-type questions with continuous response items for participants to choose from.

How often do you buy energy efficient products?
NeverAlmost neverSometimesOftenAlways
How important do you think it is to reduce your carbon footprint?
Not importantslightly importantImportantmoderately importantVery important

Because these values ​​have a natural order, they are sometimes encoded into numerical values. For example, 1 = Never, 2 = Rarely, 3 = Sometimes, 4 = Often, and 5 = Always.

But it is important to note that not all mathematical operations can be performed with these numbers. Although you can tell that two values ​​in your dataset are equal or unequal (= or ≠) or that one value is greater or less than another (< or >), you cannot meaningfully add or subtract values ​​from one another. .

This becomes relevant when collecting descriptive statistics about your data.

How to analyze ordinal data

Ordinal data can be analyzed with descriptive and inferential statistics.

descriptive statistics

you can use thesedescriptive statisticswith ordinal data:

  • hefrequency distributionin numbers or percentages,
  • hepathor themedianto find thecentral tendency,
  • herangeto indicate variability.
Ask 30 survey participants to indicate their level of agreement with the following statement:
Regular exercise is important for my mental health.
strongly disagreeI disagreeneither disagree nor agreeTo acceptTotally agree

To get an overview of your data, you can create a frequency distribution table that tells you how many times each answer was selected.

level of agreementFrequency
strongly disagree2
I disagree2
neither disagree nor agree8
To accept13
Totally agree5

To visualize your data, you can present it in a bar chart. Plot your categories on the x-axis and frequencies on the y-axis.

Unlike nominal data, the order of categories is important when displaying ordinal data.

What is ordinal data? | Examples &amp; Definitions (2)

central tendency

Hecentral tendencyof your dataset is where most of your values ​​are found. The mode, mean, and median are the three most commonly used measures of central tendency.

while thepathcan almost always be found for ordinal data, themediancan only be found in some cases.

The mean cannot be calculated with ordinal data.find the averagerequires you to perform arithmetic operations like addition and division on the dataset values. As differences between adjacent scores are unknown with ordinal data, these operations cannot be performed to obtain meaningful results.

The mode of your data is the value that appears most often.

In the current dataset, the mode isTo accept.

(Video) Types of Data: Nominal, Ordinal, Interval/Ratio - Statistics Help

Medians for even and odd data sets are found in different ways.

  • In a data set with odd numbers, the median is the value in the middle of your data set when sorted.
  • In a data set with even numbers, the median is the average of the two values ​​in the middle of your data set.
Sort all data values ​​and find the middle of your data set to find the median.

Since there are 30 values, there are 2 values ​​in the middle at positions 15 and 16. Both values ​​are equal, so the median isTo accept.

Now, suppose the two values ​​in the middle were Agree and Strongly Agree. How would you find the average of these two values?

Since you can't add or divide, you can't find the average of these two values, even if you encoded them numerically. In this case there is no median.

Variability

to evaluate thevariabilityIn your dataset, you can find the minimum, maximum, and range. You will need to numerically encode your data for this.

First, code your data by assigning a number to each response, from smallest to largest:
  • 1 = strongly disagree
  • 2 = Disagree
  • 3 = Neither disagree nor agree
  • 4 = agree
  • 5 = Strongly Agree

To find the minimum and maximum, find the lowest and highest values ​​that appear in your dataset. The minimum is 1 and the maximum is 5.

For the range, subtract the minimum from the maximum:

Range = 5 - 1 =4

The range gives you a general idea of ​​how widely your scores differ from each other. From this information, you can conclude that there was at least one response at each end of the scale.

statistical tests

inferential statisticshelp you test scientific hypotheses about your data. more apropriatestatistical testsFor ordinal data, focus on the ranks of your measures. These are non-parametric tests.

Parametric tests are used when your data meets certain criteria such asnormal distribution. While parametric tests assess means, non-parametric tests typically assess medians or ranges.

There are many possible statistical tests you can use for ordinal data. Which one you choose depends on your goals and the number and type of samples.

nonparametric testLookSamples or VariablesExample
medium humor testCompare the medians2 or more samplesHow different are the average income levels of people in 2 neighboring cities?
Mann-Whitneytutest (Wilcoxon rank sum test)Compare Sum of Score Rankings2 independent samplesHow does perceived social status in one city differ from another?
Wilcoxon Paired Pairs Signed Rank TestCompare the magnitude and direction of difference between score distributions2 dependent samplesHow similar are the distributions of income levels for Democrats and Republicans in the same city?
Kruskal-WallisHtrialCompare average score ratings3 or more samplesHow does perceived social status differ between Democrats, Republicans, and Independents?
Spearman's Rho or Rank Correlation CoefficientCorrelate 2 variables2 ordinal variablesDoes income level correlate with perceived social status?

Common questions

What is ordinal data?

ordinal datahas two characteristics:

  • Data can be sorted into different categories within a variable.
  • Categories have a natural sort order.

Unlike interval data, however, the distances between categories are uneven or unknown.

(Video) Nominal, Ordinal, Interval & Ratio Data: Simple Explanation With Examples
What are the four levels of measurement?

measurement levelstell it how accurately the variables are registered. There are 4 measurement levels, which can be ranked from lowest to highest:

  • Nominal:data can only be categorized.
  • Ordinal:data can be categorized and sorted.
  • Interval:data can be categorized and sorted, and evenly spaced.
  • Relationship:data can be categorized, sorted, evenly spaced, and has a natural zero.
What is the difference between nominal and ordinal data?

Nominal and ordinal are two of the fourmeasurement levels.Nominal level datacan only be classified, whileordinal level dataThey can be sorted and sorted.

Are ordinal variables categorical or quantitative?

In statistics,ordinalynominalboth variables are consideredcategorical variables.

Although ordinal data can sometimes be numeric, not all mathematical operations can be performed on it.

Are Likert scales ordinal or interval scales?

Individual Likert-type questions are generally consideredordinal data, because the elements have a clear sort order but do not have a uniform distribution.

In generalLikert scalescores are sometimes treated as interval data. These scores are considered to have directionality and uniform spacing between them.

The data type determines whatstatistical testsyou should use to analyze your data.

(Video) Scales of Measurement - Nominal, Ordinal, Interval, Ratio (Part 1) - Introductory Statistics

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What is ordinal data? | Examples &amp; Definitions (3)

Pritha Bhandari

Pritha has academic backgrounds in English, psychology and cognitive neuroscience. As an interdisciplinary researcher, she enjoys writing articles that explain complicated research concepts to students and academics.

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