Nominal Variable

A nominal variable classifies data into separate groups that do not have a specific ranking or order. It is used with nominal data as it is non-numerical. For instance, let us consider the variable hair color. Black, white, and brown are the possible categories, and there is no inherent order to these categories. Nominal variables can be represented using codes, but arithmetic operations cannot be performed on them.

Nominal variable examples:

1. An example of a nominal variable is hair color. Hair can come in various shades such as blonde, black, brown, or red. These categories have no meaningful order, and mathematical operations cannot be applied to them.

2. Let us take the variable "favorite ice cream flavor." The categories could include chocolate, vanilla, and strawberry. These categories have no natural order—chocolate is not automatically considered better or worse than vanilla or strawberry.

3. Similarly, some common examples of nominal data include:

• Eye Color: Blue, Brown, Green, Hazel, Black
• Type of Pet: Cat, Dog, Bird, Fish, Hamster
• Nationality: Indian, Chinese, American, Australian, Canadian
• Political Party: Republican, Democratic, Green, Independent
• Blood Type: O, A, B, AB

A nominal scale is a measurement level that deals exclusively with qualitative variables. It uses labels or tags to categorize objects rather than measure them numerically. Along with nominal, there are three other types of measurement scales: ordinal, interval, and ratio. A nominal variable belongs to this scale, and if a number is assigned to an object, it simply acts as a label with a one-to-one correspondence rather than carrying any quantitative meaning.

Therefore, the variables on a nominal scale do not possess any numerical properties.

Example:
 

• Favorite ice cream flavor: “In the survey, respondents indicated their preferred ice cream flavor as chocolate, vanilla, strawberry, or mint. These categories serve only as names of flavors and cannot be arranged in any particular order.”
   
• Type of smartphone used: “The students were grouped based on the smartphone brand they owned: Apple, Samsung, Huawei, or Google. Each brand acts as a label and carries no numerical or ranking value.”
   
• Customer service feedback categories: “Customer complaints were organized into groups such as technical issue, billing problem, delayed delivery, or defective product. These categories classify the nature of the complaint without any hierarchical meaning.”

Binary variables: Binary type represents a categorical variable that can have only one of the two possible categories (response or outcome).

For instance, a question such as "Q: Do you have a car driving license?" can be answered by "Yes" or "No." Likewise, a medical test result could be "Positive" or "Negative". In data analysis, these variables are typically modelled as binary (True/False) or as 0s and 1s.

Multiple category variables: Polytomous category variables are categorical variables with more than two (unordered) response categories, where each level is equally likely.

Examples are questions of the form, "What is your race? With answers such as British, Asian, African, or American" and the question "What is your marital status?", the choices are Single, Married, Divorced, or Widowed. These are properties of the elements of x such that no ordering is inferred.

Ordered nominal variables: As part of nominal variables, ordered nominal subtypes are such that the values have an associated logical ordering or ranking. But is there a way to measure or determine whether the gap between them is considered the same?

For instance, when you ask, "Would you recommend our product to others?" answers could be "Very likely" to "Very unlikely", with "Very likely" being the highest recommendation, 64, and 'Extremely Unlikely' the lowest.

Unordered nominal variables: For unordered nominal data, such as categories without a clear ordering, the level or rank would not make sense. All of these are equally important, and not in any order.

For instance, if a question is about payment method preference, the answer could be cash, credit card, debit card, online banking, PayPal, and so on. Likewise, when you ask where someone heard about a job, possible responses might be LinkedIn, Indeed, the company's website, and so on.

Some characteristics of a nominal variable are:
 

• A nominal variable classifies data with no inherent order or ranking.
   
• These are meant to be meaningful names or labels, not numbers, by convention.
   
• Every observation belongs to precisely one of these mutually exclusive categories.
   
• Nominal variables cannot be added or subtracted, multiplied or divided, or analyzed with more complex statistical techniques.
   
• Qualitative variables are categorical variables without numerical values.
   
• We use nominal variables to take surveys, databases, and research studies.

• Pandas: A widely used data analysis library for Python that has wide-ranging support for categorical data in the form of astype('category'), grouping, frequency tables, and cross-tabulations (value_counts(), crosstab(), etc.). Pandas commonly encodes and decodes nominal variables, summarizes the distribution of categorical values, and creates contingency tables for categorical data.
   
• NumPy: It is often the first data manipulation library people encounter. It provides high-performance numerical computations and can handle object and categorical types as arrays. Most other libraries (especially pandas) are built on NumPy, which is used for preprocessing data before analysis. This is efficient for numerical computing.
   
• Matplotlib: As a low-level library, Matplotlib can be used to make any of the plots provided by default in seaborn. It helps plot specific categorical plots when more control than seaborn provides out of the box is required. Typical uses are pie charts and mixed plots.
   
• Category_encoders: A feature engineering library that implements the advanced techniques of categorical variable encoding: target encoding, Helmert encoding, binary encoding, and hashing encoding. This library can be handy for handling high-cardinality nominal variables (i.e., variables with many unique values) in machine learning models. These encodings improve the performance of machine learning models when converting categorical features into numerical inputs.
   
• Polars: An alternative to Pandas that's faster and provides a similar API. There are also functions for manipulating categorical data, which help efficiently store and handle large amounts of nominal data.

Categorical variables are classified into nominal, ordinal, and dichotomous variables. Nominal variables classify data without any numerical value or ranking, while ordinal variables are used to categorize data with a specific order or ranking. The main differences between the nominal variable and the ordinal variable are listed below:
 

• A nominal variable is qualitative and has no numerical order, whereas an ordinal variable is qualitative but has a specific order or ranking.
   
• The data of an ordinal variable can be ordered or ranked. For example, data from research or a survey can be considered ordinal data. 
   
• The data of a nominal variable can be categorized into distinct categories without any inherent ordering or numerical value. 
   
• Nominal variables are used to classify and label variables, such as name, color, zip code, and so on. 
   
• An ordinal variable contains variables like educational and economic status, and customer satisfaction level. 
   
• Mode is the only measure of central tendency used with nominal variables. Ordinal variables can also be analyzed using the median, mode, quantiles, and percentiles.  
   

Nominal variables categorize data without any specific order or hierarchy. Therefore, nominal variables are analyzed by different techniques such as comparing the frequencies, grouping, and counting. The methods of nominal variable analysis vary depending on the size of the dataset, research problem, and data quality. The most common techniques to analyze nominal variables are:

• Frequency distribution:This method includes finding the different categories and counting how many times each category occurs. To understand the data patterns and trends, we can use this frequency count. For a better understanding, take a look at this example. We took a survey of 50 people about their favorite ice cream, and we found the following results:
  
  20 people: Vanilla 
  12 people: Chocolate
  18 people: Strawberry 
  
  Through frequency distribution, we can see which category is the most or least common. 
   
• Central tendency:This technique involves finding the most frequently occurring category in a dataset. Central tendency identifies the mode, which represents the most popular category. Also, it is used to express how different and similar the distributions of categories are in the sample.
  
  For instance, in a survey of 100 people, if 60 people choose “orange”, 30 choose “apple”, and 10 choose “watermelon”, then orange is the mode. Because it appears the most in the given dataset. 
   
• Chi-square test: To check the relationship between two nominal variables, we use the chi-square test. This statistical test is used to determine the significant connection between two categorical variables. The actual number of times each category appears is calculated and then compared with the expected number of times each category appears. It helps to determine whether they are related or randomly distributed.  The formula for finding chi-square is χ² = Σ((O−E)²/E). 
  
  For example, we can find answers to questions like, does a person’s age affect their favorite flavor of ice cream?
   
• Contingency table analysis: This is a cross-tabulation technique that involves comparing two variables to see their relationships. This is a method of constructing rows and columns with variables. For each combination of categories, there is a frequency count of occurrences that highlights the relationship between the two categories. For instance, if we analyze favorite movies vs. gender, the table might show that more men prefer action movies while more women prefer feel-good movies. 

Nominal variables play a crucial role in different fields, such as marketing, healthcare, and social sciences. Understanding how to represent nominal variables is important for categorizing data for a clear interpretation. Some common methods for representing nominal data are:
 

Frequency tables: Frequency tables give a list of every category along with its frequency (count). Frequency tables provide a clear and accurate representation of nominal data. For example, if we survey 60 people about their favorite ice cream flavor, we can create a frequency table.

This table will help us understand and compare the responses for each category. 

Visualization charts: Bar charts and pie charts are highly effective for visually representing the distribution of nominal data. Bar charts provide a clear comparison of values across categories by using bars whose lengths correspond to numerical values, making it easier to interpret precise differences. Pie charts, on the other hand, excel at showing part-to-whole relationships and are visually appealing for conveying proportions, especially when there are few distinct categories. For more insights and detailed techniques on data visualization, you can explore the data visualization cheat sheet. Additionally, learning comprehensive statistical approaches can further enhance your data analysis skills.
 

Bar chart: We use a bar chart to express the category frequencies. Bar charts are one of the simplest forms to represent nominal data. It is used to symbolize each category, and the bar’s height and length reflect the count or frequency of each category. For example, if we ask 200 people about their favorite fruits, then they respond with Apple, Banana, Orange, Strawberry, and Grape. So the bar chart is as follows: 

Pie charts: Pie charts explain the category proportions as slices of a circle. It represents the data in a circular format. To represent the parts of a whole dataset, we can use pie charts. For instance, if we survey 60 people about their favorite ice cream flavor and the data is as follows:  

So, the pie chary of the data is:
 

Nominal variables are categorical variables without any order or numerical value. The process of collecting nominal data involves gathering qualitative variables for a dataset, and it involves several methods. They are:

 
Surveys and questionnaires: Create surveys that include multiple-choice questions, so that the respondents can choose their answer from the predefined categories.

For example, which mobile phone brand do you prefer? 

Samsung
Apple 
Google Pixel 
OnePlus

Interviews: Ask structured or semi-structured questions to get categorical responses. For instance, asking interviewees about their educational status or marital status. Also, we can ask open-ended and closed-ended questions.

Observation: Observe and record data about targeted respondents and categorize them for future purposes. For instance, observing youngsters and their clothing preferences and trends. 

Administrative records: Using the existing records or documents to collect the nominal data. For example, school records with the student’s name and education level can be utilized for obtaining categorized information.

Online forms: Design online forms with radio buttons to collect categorical responses. For instance, a Google form asking for education level, with options, high school, higher secondary, undergraduate, and graduate.

Here are some student, teacher, and parent-friendly, intuitive, and fun tips and tricks that will help learners master the nominal variable. 

1. Nominal variables are easiest for students to understand when linked to familiar everyday categories. Teachers can use everyday examples, such as favorite fruit, eye color, types of pets, shoe brands, and favorite school subjects.
    
2. After students create frequency tables, teachers and parents ask them to identify which category occurs most frequently and which occurs least frequently. This method would help develop early analytical skills.
    
3. Parents should encourage students to conduct small surveys on topics like favorite cartoons, snacks, or sports, and then have them classify and tally their responses, making the concept of data classification tangible and engaging.
    
4. Parents can aid the students by supplying objects or pictures for students to classify – perhaps, baby animals, shapes, colors of food – which is a tactile way to understand classification and what lies at the heart of nominal variables.
    
5. Teachers and parents may assign colors to categorize as they work on problems. For instance, red for apple, yellow for banana and green for grapes. This strategy is an easy and colorful way to help students understand the differences in categories.

Nominal variables help us to categorize data into categories without any ranking. The real-life applications of nominal variables are countless. They are:
 

• To learn about the trends and patterns in a market industry, businesses use nominal variables like favorite brands, color, nationality, and gender to divide their customers. 
   
• A medical professional uses different nominal variables such as the patient’s blood type, disease type, or medication type. It will help them to segment their patients and decide on better treatment plans. 
   
• To analyze player performance, nominal variables such as team name, jersey color, or position are used for classification purposes. 
   
• In the fields of political science, e-commerce, social media marketing, and even law enforcement, professionals use different nominal variables to categorize their data.