Statistics for Data Science

  1. Inferential Statistics: From Samples to Populations
    1. Sampling Methods and Design
      1. Probability Sampling Methods
        1. Simple Random Sampling
          1. Definition and Procedure
            1. Random Number Generation
              1. Advantages and Limitations
                1. When to Use
                2. Stratified Sampling
                  1. Definition and Rationale
                    1. Stratum Formation Criteria
                      1. Proportional Allocation
                        1. Optimal Allocation
                          1. Advantages and Applications
                          2. Cluster Sampling
                            1. Definition and Procedure
                              1. Single-Stage vs. Multi-Stage
                                1. Cluster Formation Considerations
                                  1. Cost-Effectiveness
                                    1. Applications in Large Populations
                                    2. Systematic Sampling
                                      1. Definition and Procedure
                                        1. Sampling Interval Calculation
                                          1. Starting Point Selection
                                            1. Advantages and Risks
                                              1. Periodic Patterns Concern
                                            2. Non-Probability Sampling Methods
                                              1. Convenience Sampling
                                                1. Purposive Sampling
                                                  1. Quota Sampling
                                                    1. Snowball Sampling
                                                    2. Sampling Bias and Errors
                                                      1. Selection Bias
                                                        1. Undercoverage Bias
                                                          1. Nonresponse Bias
                                                            1. Voluntary Response Bias
                                                            2. Measurement Bias
                                                              1. Response Bias
                                                                1. Interviewer Bias
                                                                  1. Social Desirability Bias
                                                                  2. Sampling Error vs. Non-Sampling Error
                                                                    1. Random vs. Systematic Errors
                                                                      1. Error Reduction Strategies
                                                                    2. Sample Size Determination
                                                                      1. Factors Affecting Sample Size
                                                                        1. Margin of Error Considerations
                                                                          1. Confidence Level Impact
                                                                            1. Population Variability
                                                                              1. Cost-Benefit Analysis
                                                                            2. Estimation Theory
                                                                              1. Point Estimation
                                                                                1. Definition and Concept
                                                                                  1. Single Value Estimates
                                                                                    1. Estimator vs. Estimate
                                                                                    2. Common Point Estimators
                                                                                      1. Sample Mean for Population Mean
                                                                                        1. Sample Proportion for Population Proportion
                                                                                          1. Sample Variance for Population Variance
                                                                                          2. Properties of Estimators
                                                                                            1. Unbiasedness
                                                                                              1. Definition and Importance
                                                                                                1. Bias Calculation
                                                                                                  1. Unbiased vs. Biased Estimators
                                                                                                  2. Efficiency
                                                                                                    1. Minimum Variance Property
                                                                                                      1. Relative Efficiency
                                                                                                        1. Cramér-Rao Lower Bound
                                                                                                        2. Consistency
                                                                                                          1. Convergence in Probability
                                                                                                            1. Large Sample Behavior
                                                                                                              1. Relationship to Unbiasedness
                                                                                                              2. Sufficiency
                                                                                                                1. Complete Information Usage
                                                                                                                  1. Minimal Sufficient Statistics
                                                                                                                2. Method of Moments
                                                                                                                  1. Principle and Procedure
                                                                                                                    1. Moment Equations
                                                                                                                      1. Applications and Examples
                                                                                                                      2. Maximum Likelihood Estimation
                                                                                                                        1. Likelihood Function
                                                                                                                          1. Log-Likelihood
                                                                                                                            1. MLE Properties
                                                                                                                          2. Interval Estimation
                                                                                                                            1. Confidence Intervals Concept
                                                                                                                              1. Interval vs. Point Estimates
                                                                                                                                1. Confidence Level Interpretation
                                                                                                                                  1. Common Misconceptions
                                                                                                                                    1. Frequentist Interpretation
                                                                                                                                    2. Confidence Level Selection
                                                                                                                                      1. 90%, 95%, 99% Common Choices
                                                                                                                                        1. Trade-offs with Interval Width
                                                                                                                                          1. Context-Dependent Decisions
                                                                                                                                          2. Constructing Confidence Intervals for Means
                                                                                                                                            1. Known Population Variance
                                                                                                                                              1. Z-Distribution Usage
                                                                                                                                                1. Formula and Calculation
                                                                                                                                                  1. Assumptions Required
                                                                                                                                                  2. Unknown Population Variance
                                                                                                                                                    1. t-Distribution Usage
                                                                                                                                                      1. Degrees of Freedom
                                                                                                                                                        1. Small vs. Large Samples
                                                                                                                                                        2. Large Sample Approximations
                                                                                                                                                        3. Constructing Confidence Intervals for Proportions
                                                                                                                                                          1. Normal Approximation Method
                                                                                                                                                            1. Success-Failure Condition
                                                                                                                                                              1. Continuity Correction
                                                                                                                                                                1. Wilson Score Interval
                                                                                                                                                                  1. Exact Methods for Small Samples
                                                                                                                                                                  2. Confidence Intervals for Variance
                                                                                                                                                                    1. Chi-Square Distribution Usage
                                                                                                                                                                      1. Asymmetric Intervals
                                                                                                                                                                        1. Sensitivity to Normality
                                                                                                                                                                        2. Margin of Error
                                                                                                                                                                          1. Definition and Calculation
                                                                                                                                                                            1. Factors Affecting Margin of Error
                                                                                                                                                                              1. Sample Size Impact
                                                                                                                                                                                1. Confidence Level Impact
                                                                                                                                                                                  1. Population Variability Impact
                                                                                                                                                                                  2. Interpretation and Communication
                                                                                                                                                                                    1. Sample Size Planning
                                                                                                                                                                                  3. Bootstrap Methods
                                                                                                                                                                                    1. Bootstrap Principle
                                                                                                                                                                                      1. Resampling Procedure
                                                                                                                                                                                        1. Bootstrap Confidence Intervals
                                                                                                                                                                                          1. Advantages and Limitations

                                                                                                                                                                                      Previous

                                                                                                                                                                                      4. Probability Distributions

                                                                                                                                                                                      Go to top

                                                                                                                                                                                      Next

                                                                                                                                                                                      6. Hypothesis Testing