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. never  2. Rarely  3. Sometimes  4. Often  5. 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
 measurement levels
 Examples of ordinal scales
 How to collect ordinal data
 How to analyze ordinal data
 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.
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).
Variable  ordinal values 

language ability 

level of agreement 

income level 

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 ask  options 

How old are you? 

what is your education level? 

In the last three months, how many times did you buy groceries online? 

Choice of measurement level
Some types of data can be recorded at more than one level. For example, for the age variable:
 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 usingLikerttype scales. Likert scales are made up of 4 or more Likerttype questions with continuous response items for participants to choose from.
How often do you buy energy efficient products?  

Never  Almost never  Sometimes  Often  Always 
How important do you think it is to reduce your carbon footprint?  
Not important  slightly important  Important  moderately important  Very 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.
Regular exercise is important for my mental health.  

strongly disagree  I disagree  neither disagree nor agree  To accept  Totally 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 agreement  Frequency 

strongly disagree  2 
I disagree  2 
neither disagree nor agree  8 
To accept  13 
Totally agree  5 
To visualize your data, you can present it in a bar chart. Plot your categories on the xaxis and frequencies on the yaxis.
Unlike nominal data, the order of categories is important when displaying ordinal data.
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.
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.
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.
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 nonparametric tests.
Parametric tests are used when your data meets certain criteria such asnormal distribution. While parametric tests assess means, nonparametric 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 test  Look  Samples or Variables  Example 

medium humor test  Compare the medians  2 or more samples  How different are the average income levels of people in 2 neighboring cities? 
MannWhitneytutest (Wilcoxon rank sum test)  Compare Sum of Score Rankings  2 independent samples  How does perceived social status in one city differ from another? 
Wilcoxon Paired Pairs Signed Rank Test  Compare the magnitude and direction of difference between score distributions  2 dependent samples  How similar are the distributions of income levels for Democrats and Republicans in the same city? 
KruskalWallisHtrial  Compare average score ratings  3 or more samples  How does perceived social status differ between Democrats, Republicans, and Independents? 
Spearman's Rho or Rank Correlation Coefficient  Correlate 2 variables  2 ordinal variables  Does 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 Likerttype 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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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.