Statistics

1. Inferential Statistics
   1. Sampling Theory
      1. Probability Sampling
         1. Simple Random Sampling
            1. Definition and Characteristics
            2. Advantages and Disadvantages
            3. Implementation in Practice
         2. Stratified Sampling
            1. Purpose and Approaches
            2. Stratification Criteria
            3. Proportional vs. Disproportional Stratified Sampling
         3. Systematic Sampling
            1. Systematic Selection Process
            2. Interval Selection
            3. Use Cases and Limitations
         4. Cluster Sampling
            1. Definition and Applications
            2. Single-stage and Multi-stage Cluster Sampling
            3. The Impact of Intracluster Correlation
      2. Non-probability Sampling
         1. Convenience Sampling
            1. Situations for Use
            2. Potential Biases and Limitations
         2. Quota Sampling
            1. Definition and Examples
            2. Quota Setting and Execution
         3. Judgment Sampling
            1. Expert Decision-making in Sampling
            2. Subjectivity Issues
   2. Estimation Theory
      1. Point Estimation
         1. Properties of Good Estimators
            1. Unbiasedness
            2. Consistency
            3. Efficiency
            4. Sufficiency
         2. Methods of Point Estimation
            1. Method of Moments
            2. Maximum Likelihood Estimation
      2. Interval Estimation
         1. Purpose and Importance
         2. Interpretation and Use Cases
      3. Confidence Intervals
         1. Definition and Calculation
         2. Confidence Levels and Their Implications
         3. Constructing Confidence Intervals for Different Parameters
            1. Mean, Proportion, Variance
   3. Hypothesis Testing
      1. Null and Alternative Hypotheses
         1. Defining and Testing Hypotheses
         2. Formulation Techniques
         3. Examples in Different Contexts
      2. Type I and Type II Errors
         1. Definitions and Impact
         2. Trade-off Between Error Types
         3. Controlling Errors in Testing
      3. Significance Level (Alpha)
         1. Choosing the Level of Significance
         2. Implications of Alpha Level Selection
      4. p-values
         1. Definition and Interpretation
         2. Common Misconceptions
         3. Relationship with Alpha Level
      5. Power of a Test
         1. Definition and Importance
         2. Calculating Power
         3. Factors Influencing Power
   4. Parametric Tests
      1. t-tests
         1. One-sample t-test
            1. When and How to Use
            2. Assumptions and Calculations
         2. Independent two-sample t-test
            1. Comparing Means Between Two Groups
            2. Assumptions of Variance Equality
         3. Paired t-test
            1. Contexts for Use
            2. Paired Data and Assumptions
      2. ANOVA
         1. One-way ANOVA
            1. Definition and Uses
            2. Assumptions and Results Interpretation
         2. Two-way ANOVA
            1. Dealing with Two Factors
            2. Interaction Effects and Interpretation
   5. Non-parametric Tests
      1. Wilcoxon Tests
         1. Wilcoxon Signed-Rank Test
            1. Applications and Calculation
            2. Assumptions and Alternatives
         2. Wilcoxon Rank-Sum Test
            1. Suitable Scenarios and Implementation
      2. Kruskal-Wallis Test
         1. Non-parametric Alternative to ANOVA
         2. Use Cases and Data Requirements
      3. Mann-Whitney U Test
         1. Comparing Two Independent Samples
         2. Interpretation of Results
      4. Chi-Square Test
         1. Applications in Contingency Tables
         2. Assumptions and Calculations
         3. Goodness-of-Fit Testing