Categorical Data Analysis

Categorical data analysis is a branch of statistics focused on interpreting data that can be sorted into distinct groups or categories, such as gender, survey responses (e.g., agree, disagree), or types of products. Unlike the analysis of numerical data which often involves calculating means and standard deviations, this field utilizes frequencies, proportions, and percentages to uncover patterns and relationships. Key methods include constructing contingency tables (cross-tabulations) to visualize the intersection of two or more categorical variables and applying statistical tests, most notably the chi-squared (χ²) test, to determine if a significant association exists between them.

1. Foundations of Categorical Data
   1. Nature of Categorical Variables
      1. Definition and Characteristics
      2. Discrete Nature of Categories
      3. Qualitative vs Quantitative Distinction
   2. Types of Categorical Variables
      1. Binary Variables
         1. Definition and Properties
         2. Coding Schemes
         3. Examples in Research
      2. Nominal Variables
         1. Unordered Categories
         2. Properties and Characteristics
         3. Common Examples
      3. Ordinal Variables
         1. Ordered Categories
         2. Properties and Characteristics
         3. Natural Ordering Concept
         4. Common Examples
   3. Measurement Scales
      1. Nominal Scale
         1. Definition and Properties
         2. Equality and Difference Operations
         3. Limitations in Mathematical Operations
      2. Ordinal Scale
         1. Definition and Properties
         2. Ranking and Ordering
         3. Greater Than and Less Than Relations
      3. Comparison with Continuous Scales
         1. Interval Scale Properties
         2. Ratio Scale Properties
         3. Implications for Analysis Methods
   4. Data Collection and Coding
      1. Survey Design for Categorical Data
      2. Response Categories Design
      3. Coding Systems
      4. Missing Data Considerations