Statistical Inference

  1. Sampling and Sampling Distributions
    1. Principles of Sampling
      1. The Importance of Random Sampling
        1. Reducing Bias
          1. Ensuring Representativeness
            1. Randomization Techniques
            2. Sources of Bias in Sampling
              1. Selection Bias
                1. Response Bias
                  1. Non-response Bias
                    1. Measurement Bias
                  2. Sampling Methods
                    1. Simple Random Sampling
                      1. Definition and Procedure
                        1. With and Without Replacement
                          1. Advantages and Limitations
                          2. Stratified Sampling
                            1. Definition and Procedure
                              1. Proportional Stratification
                                1. Disproportional Stratification
                                  1. Optimal Allocation
                                  2. Cluster Sampling
                                    1. Definition and Procedure
                                      1. Single-Stage Clustering
                                        1. Multi-Stage Clustering
                                          1. Design Effects
                                          2. Systematic Sampling
                                            1. Definition and Procedure
                                              1. Periodicity and Potential Bias
                                                1. Random Start Selection
                                                2. Convenience and Purposive Sampling
                                                  1. Non-probability Sampling Methods
                                                    1. Limitations and Biases
                                                  2. Sampling Distributions
                                                    1. The Concept of a Sampling Distribution
                                                      1. Definition of Sampling Distribution
                                                        1. Sampling Distribution of a Statistic
                                                          1. Role in Statistical Inference
                                                          2. Properties of Sampling Distributions
                                                            1. Center (Expected Value)
                                                              1. Unbiased Estimators
                                                                1. Bias in Estimators
                                                                2. Spread (Standard Error)
                                                                  1. Definition of Standard Error
                                                                    1. Factors Affecting Standard Error
                                                                      1. Standard Error vs Standard Deviation
                                                                      2. Shape
                                                                        1. Skewness and Kurtosis
                                                                          1. Normality and Non-Normality
                                                                            1. Effect of Sample Size on Shape
                                                                          2. The Central Limit Theorem
                                                                            1. Statement and Conditions
                                                                              1. Requirements for CLT
                                                                                1. Sample Size Considerations
                                                                                2. Implications for the Sample Mean
                                                                                  1. Approximate Normality for Large Samples
                                                                                    1. Effect of Population Distribution
                                                                                      1. Effect of Sample Size
                                                                                      2. Implications for the Sample Proportion
                                                                                        1. Normal Approximation for Proportions
                                                                                          1. Success-Failure Condition
                                                                                          2. Implications for Other Statistics
                                                                                            1. Sample Variance
                                                                                              1. Difference of Sample Means
                                                                                            2. Common Sampling Distributions
                                                                                              1. The Normal Distribution
                                                                                                1. Properties and Parameters
                                                                                                  1. Standard Normal Distribution
                                                                                                    1. Applications in Inference
                                                                                                    2. The t-Distribution
                                                                                                      1. Properties and Parameters
                                                                                                        1. Degrees of Freedom
                                                                                                          1. Relationship to Normal Distribution
                                                                                                            1. Applications in Inference
                                                                                                            2. The Chi-Squared Distribution
                                                                                                              1. Properties and Parameters
                                                                                                                1. Degrees of Freedom
                                                                                                                  1. Relationship to Normal Distribution
                                                                                                                    1. Applications in Inference
                                                                                                                    2. The F-Distribution
                                                                                                                      1. Properties and Parameters
                                                                                                                        1. Degrees of Freedom
                                                                                                                          1. Relationship to Chi-Squared
                                                                                                                            1. Applications in Variance Comparison

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                                                                                                                      1. Foundations of Statistical Inference

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                                                                                                                      3. Point Estimation