Categorical Data

Categorical data is the data that can be represented as categories or data which can be grouped. It stores data as categories or groups using names or labels. Categorical data is also known as qualitative data. It is visually represented using bar charts, pie charts, or frequency tables.

Categorical Data Definition

Categorical data is a type of data in statistics that sorts information into distinct groups or labels based on characteristics or qualities, instead of numerical values.

Here are some examples of categorical data for students.

1. A teacher asked students about their favorite fruit. The answers were labelled in categories such as apple, banana, mango, and orange, rather than numbers. The bar chart below shows how many students chose each fruit.
   
   This data can be termed as categorical:
   The data groups students by name or label. 
   The categories are distinct. 
   We count the students in each category rather than measuring something numerically. 
    
2. Favorite subjects: This is another example of categorical data, where the categories are based on qualitative characteristics. The categories are Math, Science, English, Social Studies, etc.
    
3. Mode of transport: In this type of categorical data, the categories classify options based on type. The categories are bus, bicycle, car, walking, etc.
    
4. Education level: This is an example of categorical data, where the categories are ranked. The categories are primary, secondary, higher secondary, graduation, etc.
    
5. Customer satisfaction rating: In this type of categorical data, the categories are arranged in a meaningful order: poor, average, good, or excellent.

There are two main types of categorical data and they are as follows:

• Nominal Data
   
• Ordinal Data

Let us now see what they mean:

Nominal Data

Nominal data is a type of categorical data that consists of two or more categories without any kind of specific order. Nominal data cannot be quantified; that is, it cannot be put into a definite hierarchy. Variables without any quantitative value or order are labeled using nominal data.

Examples of nominal data are: 
 

• Types of fruits, including apple, banana, mango, and orange. 
• Favorite colors, with categories: red, blue, green, yellow, etc. 
• Hobbies: reading, swimming, painting, etc. 

Ordinal Data

Ordinal data is a type of categorical data with a natural order. However, the difference between the ranks may not be equal. Ordinal data is a statistical type of data which is quantitative, where variables exist in naturally occurring ordered categories.
 

Examples of ordinal data are: 
 

• Clothing sizes, and the categories will be small(S), medium(M), large(L), and extra large(XL). 
• Ranking in a competition, and the categories will be 1st place, 2nd place, 3rd place, etc.
• Socio-economic status, and the categories are low, middle, and high.

We know that the categorical data is divided into nominal data and ordinal data. While both types classify information or categories, they differ in how those categories are organized. Let us see their major differences in the table below. 
 

There are different properties for categorical data. Let us see some important ones:

• Qualitative in nature: Categorical data consists of labels, names, or categories rather than numerical values.

• No arithmetic operation: Mathematical operations such as addition, subtraction, or averaging are not applicable to categorical data.

• Can be nominal or ordinal: Nominal data are data with categories having no inherent order. Ordinal data are data with categories that have no defined interval in order.

• Mutually exclusive categories: Each data point belongs to exactly one category; that is, the categories do not overlap.

• Countable and distinct categories: The number of categories is finite and countable, and each category is different from the others. This allows for easy frequency counting, analysis, and classification of distributions on tables or charts.

• Represented using labels or symbols: Values in categorical data are expressed as text or symbols rather than numbers.

• Suitability for frequency or proportion analysis: The frequency or proportion of observations in each category can be computed. It is useful for summarizing and comparing categorical distributions.
  
  
   
• Categories are meaningful: Even if categories are given number codes like male = 1 and female = 2, those numbers are simply labels, and their numeric difference has no quantitative meaning. 
   

To calculate categorical data, we must follow the steps mentioned below:

Step 1: Collect the categorical data.

First, we have to identify and gather the categorical data from different sources. Then, we have to ensure that the data is organized in distinct categories.

Step 2: Organize the data into frequency table.

List each category along with the frequency of each category.

Step 3: Visualize the data.

Use bar charts, pie charts, or histograms to represent categorical data.

Step 4: Analyze the mode.

The mode is the category with the highest frequency.

Step 5: Use contingency tables for two categorical variables

If analyzing relationships between two categorical variables, use a contingency table.

Analysis of categorical data involves applying statistical techniques to study data grouped into categories. These categories may be nominal or ordinal, depending on their nature. Below are some commonly used methods for analyzing categorical data. 

• Frequency tables: This method is useful for counting and summarizing how many observations fall into each category.
  
   
• Cross tabulations: Cross-tabulations, or cross-tabs, are tables that display the relationship between two categorical variables by showing the counts for each category combination.
  
   
• Chi-square test: A statistical test used to check whether two categorical variables have a significant association.
  
   
• Contingency tables: A two-way table that presents the frequency distribution of two categorical variables simultaneously.
  
   
• Graphical representations: Graphical methods, such as bar and pie charts, are used to compare category proportions and distributions visually.
  
   
• Odds ratio: This method measures the strength of association between two categorical variables, often used in case-control or medical studies.
  
   
• Logistic regression: A statistical model used to analyze the effect of one or more independent variables on a categorical outcome variable.
  
   
• Multiple Correspondence Analysis (MCA): It is a multivariate technique used to study patterns among multiple nominal variables.
  
   
• Analysis of Variance (ANOVA): This method is used to analyze how different categories of a categorical variable affect the mean of a continuous variable.
  
   
• Regression analysis with categorical predictors: This method examines how categorical variables influence a continuous dependent variable, often by coding categories into dummy variables. 

A categorical variable is a statistical variable that represents data grouped into specific categories or labels. They are not expressed in numerical values with mathematical meaning; instead, they classify individuals or items based on characteristics or attributes. Here, each observation falls into one of the defined categories, which will be limited and fixed in number. Categorical variables are also known as qualitative variables or attribute variables. 

Categorical variables are either a nominal variable or an ordinal variable. Nominal variables have no natural or logical order, whereas ordinal variables follow a meaningful order or ranking. 

Examples of categorical variables include demographic characteristics (gender, religion, occupation), survey responses (yes/no), and clothing sizes (S, M, L, XL). 
 

As we all know, categorical data is very important in statistics to classify information based on its characteristics. Like any data, categorical data has its own strengths and limitations.

In statistics, categorical data represents qualities or characteristics grouped into labels or categories, whereas numerical data represents measurable quantities expressed in numbers. Let us see the major differences between categorical and numerical data. 

We have learnt that categorical data is all about qualities and characteristics, not numbers. Here are some simple tips and tricks useful for students, parents, and teachers to help master the concept of categorical data. 

• Identify the type: Students should learn the differences between nominal and ordinal categorical data. Learn that nominal has no order, and ordinal is ordered. 
  
   
• Use examples from daily life: Learners can practice with familiar examples, such as favorite foods and hobbies, to relate categories to real life.
  
   
• Count and record: For easy analysis, keep track of how many times each category occurs. Use tally marks, tables, or lists to clearly organize data.
  
   
• Visualize the data: Use bar, pie, and frequency tables to make categorical data easier to understand.
  
   
• Look for patterns: Observe which categories are more common or rare. This improves analytical skills and helps reach conclusions more easily.
  
   
• Relate to real-world scenarios: Parents and teachers can encourage children to classify the things they encounter daily, such as fruits, animals, or school subjects.
  
   
• Use visual aids: Use charts, stickers, and colored cards to make categorical data easier for young learners to grasp.
  
   
• Encourage discussions: Ask learners questions like “Which color is most popular in your class?” to develop analytical thinking.
  
   
• Make learning interactive: Incorporate games, quizzes, and classroom activities to help children remember categories more effectively.
  
   
• Connect with other subjects: Parents and teachers can show how categorical data appears in science experiments, surveys, and other math problems. 
   

The categorical data have numerous applications across various fields. Let us explore how the categorical data is used in different areas:

• Healthcare: We use categorical data to assess whether the patient has any medical conditions; this is part of the patient's diagnostic process. For example, diabetes: yes/no.
  
   
• Treatment preferences: Type of treatment received, such as medication, therapy, or surgery.
  
   
• Hospital data analysis: Number of patients by gender and insurance type.
  
   
• Marketing and consumer behavior: Businesses categorize customers by gender, location, and shopping habits. Product preferences are also analyzed using categorical data. 
  
   
• Education: Student performance is assessed by grouping students into grade categories (e.g., A, B, C, and D). Schools use categorical data to examine how students enroll in different subject streams, such as science, arts, and commerce.
  
   
• Government and public policy: Categorical data is essential for planning and decision-making in government policies.
  
   
• Population surveys: Gender, marital status, employment status.
  
   
• Voting behavior: Voters categorized by political preference or region.
  
   
• Census data: Urban vs. rural, language spoken, ethnicity.
  
   
• E-commerce: Online platforms primarily rely on categorical data to improve user experience and business decisions. These categories include user preferences, content categorization, purchase status, and ratings.