Statistics

1. Multivariate Statistics
   1. Introduction to Multivariate Statistics
      1. Definition and Scope
      2. Importance and Applications
      3. Differences from Univariate and Bivariate Statistics
   2. Multivariate Analysis of Variance (MANOVA)
      1. Concept and Objectives
      2. Assumptions and Conditions
         1. Normality
         2. Homogeneity of Covariance Matrices
         3. Independence of Observations
      3. MANOVA vs. ANOVA
      4. Steps in Conducting MANOVA
         1. Checking Assumptions
         2. Selecting the MANOVA Model
         3. Interpreting Results
      5. Applications of MANOVA
      6. Post Hoc Tests for MANOVA
   3. Principal Component Analysis (PCA)
      1. Concept and Objectives
      2. Calculation of Principal Components
         1. Covariance and Correlation Matrix
         2. Eigenvalues and Eigenvectors
      3. Interpretation of PCA Results
         1. Scree Plot
         2. Loadings and Scores
         3. Biplot
      4. Applications of PCA
         1. Dimensionality Reduction
         2. Data Visualization
         3. Feature Extraction
      5. Limitations and Considerations of PCA
   4. Factor Analysis
      1. Exploratory Factor Analysis (EFA)
         1. Objectives and Methodology
         2. Determining the Number of Factors
         3. Factor Rotation Techniques
            1. Varimax
            2. Promax
         4. Interpretation of Factor Loadings
      2. Confirmatory Factor Analysis (CFA)
         1. Objectives and Methodology
         2. Model Specification and Identification
         3. Goodness-of-Fit Measures
      3. Applications and Limitations of Factor Analysis
   5. Cluster Analysis
      1. Types of Cluster Analysis
         1. Hierarchical Clustering
            1. Agglomerative Methods
            2. Divisive Methods
         2. Non-Hierarchical Clustering
            1. k-means Clustering
            2. Medoids Clustering
      2. Choosing the Number of Clusters
      3. Similarity and Distance Measures
         1. Euclidean Distance
         2. Manhattan Distance
         3. Cosine Similarity
      4. Applications of Cluster Analysis
         1. Market Segmentation
         2. Image Processing
         3. Biomedical Research
      5. Limitations and Challenges
   6. Discriminant Analysis
      1. Linear Discriminant Analysis (LDA)
         1. Objective and Methodology
         2. Assumptions and Conditions
         3. Steps in Conducting LDA
      2. Quadratic Discriminant Analysis (QDA)
         1. Differences from LDA
         2. Assumptions and Conditions
      3. Applications of Discriminant Analysis
         1. Credit Scoring
         2. Pattern Recognition
         3. Medical Diagnosis
   7. Canonical Correlation Analysis
      1. Concept and Objectives
      2. Calculation and Interpretation
      3. Applications and Case Studies
   8. Structural Equation Modeling (SEM)
      1. Concepts and Terminology
         1. Latent Variables
         2. Path Diagrams
      2. Steps in SEM
         1. Model Specification
         2. Estimation
         3. Model Evaluation
      3. Applications and Limitations
   9. Multidimensional Scaling (MDS)
      1. Concept and Objectives
      2. Steps in MDS
         1. Distance Matrix Calculation
         2. Configuration of Points in Low-Dimensional Space
      3. Applications of MDS
         1. Market Research
         2. Perceptual Mapping
         3. Cognitive Science
   10. Application Domains of Multivariate Statistics
       1. Business and Marketing
          1. Consumer Behavior Analysis
          2. Product Launches and Surveys
       2. Healthcare and Medicine
          1. Biomedical Statistics
          2. Epidemiological Studies
       3. Social Sciences
          1. Sociodemographic Research
          2. Psychometrics
       4. Environmental Analysis
          1. Climate Data Analysis
          2. Ecological Pattern Recognition
   11. Challenges and Considerations
       1. High Dimensionality
       2. Collinearity and Multicollinearity
       3. Sample Size Requirements
       4. Interpretation Complexity