Quantitative Methods

  1. Inferential Statistics
    1. Sampling Theory
      1. Population vs Sample
        1. Definitions
          1. Parameters vs Statistics
          2. Sampling Methods
            1. Simple Random Sampling
              1. With Replacement
                1. Without Replacement
                  1. Implementation
                  2. Systematic Sampling
                    1. Procedure
                      1. Sampling Interval
                        1. Potential Bias
                        2. Stratified Sampling
                          1. Proportional Allocation
                            1. Optimal Allocation
                              1. Advantages
                              2. Cluster Sampling
                                1. Single-stage Clustering
                                  1. Multi-stage Clustering
                                    1. Design Effects
                                    2. Multistage Sampling
                                      1. Design Considerations
                                        1. Weighting
                                      2. Sampling Distributions
                                        1. Sampling Distribution of the Mean
                                          1. Standard Error
                                          2. Central Limit Theorem
                                            1. Statement
                                              1. Conditions
                                              2. Sampling Distribution of Proportions
                                                1. Normal Approximation
                                                2. Sampling Distribution of Variance
                                                  1. Chi-square Distribution
                                              3. Estimation Theory
                                                1. Point Estimation
                                                  1. Estimators vs Estimates
                                                    1. Method of Moments
                                                      1. Maximum Likelihood Estimation
                                                        1. Properties of Estimators
                                                          1. Unbiasedness
                                                            1. Efficiency
                                                              1. Consistency
                                                                1. Sufficiency
                                                              2. Interval Estimation
                                                                1. Confidence Intervals
                                                                  1. Interpretation
                                                                    1. Confidence Level
                                                                      1. Confidence Coefficient
                                                                      2. Confidence Intervals for Means
                                                                        1. Known Population Variance
                                                                          1. Unknown Population Variance
                                                                            1. Small Sample Considerations
                                                                            2. Confidence Intervals for Proportions
                                                                              1. Large Sample Methods
                                                                                1. Small Sample Methods
                                                                                  1. Wilson Score Interval
                                                                                  2. Confidence Intervals for Variance
                                                                                    1. Chi-square Based Intervals
                                                                                    2. Sample Size Determination
                                                                                      1. For Means
                                                                                        1. For Proportions
                                                                                          1. Power Considerations
                                                                                      2. Hypothesis Testing
                                                                                        1. Fundamental Concepts
                                                                                          1. Statistical Hypotheses
                                                                                            1. Null Hypothesis
                                                                                              1. Alternative Hypothesis
                                                                                                1. Simple vs Composite Hypotheses
                                                                                                2. Test Statistics
                                                                                                  1. Distribution Under Null Hypothesis
                                                                                                  2. Critical Regions
                                                                                                    1. One-tailed Tests
                                                                                                      1. Two-tailed Tests
                                                                                                        1. Critical Values
                                                                                                        2. Decision Rules
                                                                                                          1. Rejection Criteria
                                                                                                            1. Non-rejection Criteria
                                                                                                          2. Errors and Power
                                                                                                            1. Type I Error
                                                                                                              1. Significance Level
                                                                                                              2. Type II Error
                                                                                                                1. Beta Risk
                                                                                                                2. Statistical Power
                                                                                                                  1. Factors Affecting Power
                                                                                                                    1. Power Curves
                                                                                                                    2. Sample Size and Power
                                                                                                                      1. Power Analysis
                                                                                                                        1. Effect Size
                                                                                                                      2. Tests for Single Populations
                                                                                                                        1. Tests for Population Mean
                                                                                                                          1. Z-test (Known Variance)
                                                                                                                            1. t-test (Unknown Variance)
                                                                                                                              1. Assumptions
                                                                                                                              2. Tests for Population Proportion
                                                                                                                                1. Large Sample Test
                                                                                                                                  1. Exact Test
                                                                                                                                  2. Tests for Population Variance
                                                                                                                                    1. Chi-square Test
                                                                                                                                      1. Assumptions
                                                                                                                                    2. Tests for Two Populations
                                                                                                                                      1. Comparing Two Means
                                                                                                                                        1. Independent Samples
                                                                                                                                          1. Equal Variances
                                                                                                                                            1. Unequal Variances
                                                                                                                                              1. Welch's t-test
                                                                                                                                              2. Paired Samples
                                                                                                                                                1. Paired t-test
                                                                                                                                                  1. Assumptions
                                                                                                                                                2. Comparing Two Proportions
                                                                                                                                                  1. Independent Samples
                                                                                                                                                    1. Paired Samples
                                                                                                                                                    2. Comparing Two Variances
                                                                                                                                                      1. F-test
                                                                                                                                                        1. Assumptions
                                                                                                                                                      2. Analysis of Variance
                                                                                                                                                        1. One-Way ANOVA
                                                                                                                                                          1. Model Assumptions
                                                                                                                                                            1. F-statistic
                                                                                                                                                              1. Sum of Squares Decomposition
                                                                                                                                                                1. Mean Squares
                                                                                                                                                                2. Two-Way ANOVA
                                                                                                                                                                  1. Main Effects
                                                                                                                                                                    1. Interaction Effects
                                                                                                                                                                      1. Model Assumptions
                                                                                                                                                                      2. Multiple Comparisons
                                                                                                                                                                        1. Family-wise Error Rate
                                                                                                                                                                          1. Bonferroni Correction
                                                                                                                                                                            1. Tukey's HSD
                                                                                                                                                                              1. Scheffe's Method
                                                                                                                                                                            2. Non-parametric Tests
                                                                                                                                                                              1. When to Use Non-parametric Tests
                                                                                                                                                                                1. Assumption Violations
                                                                                                                                                                                  1. Ordinal Data
                                                                                                                                                                                  2. Tests for Single Samples
                                                                                                                                                                                    1. Sign Test
                                                                                                                                                                                      1. Wilcoxon Signed-Rank Test
                                                                                                                                                                                      2. Tests for Two Independent Samples
                                                                                                                                                                                        1. Mann-Whitney U Test
                                                                                                                                                                                          1. Kolmogorov-Smirnov Test
                                                                                                                                                                                          2. Tests for Multiple Samples
                                                                                                                                                                                            1. Kruskal-Wallis Test
                                                                                                                                                                                              1. Friedman Test
                                                                                                                                                                                              2. Tests for Association
                                                                                                                                                                                                1. Chi-square Test of Independence
                                                                                                                                                                                                  1. Fisher's Exact Test
                                                                                                                                                                                                    1. Chi-square Goodness-of-Fit Test

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                                                                                                                                                                                              1. Foundations of Quantitative Analysis

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                                                                                                                                                                                              3. Correlation and Regression Analysis