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Statistics
Social Statistics
1. Introduction to Social Statistics
2. Fundamental Concepts
3. Data Collection Methods
4. Sampling Techniques
5. Data Management and Preparation
6. Descriptive Statistics: Univariate Analysis
7. Foundations of Inferential Statistics
8. Estimation and Confidence Intervals
9. Hypothesis Testing
10. Testing for Differences Between Means
11. Analysis of Categorical Data
12. Bivariate Correlation and Regression
13. Multivariate Regression
14. Advanced Topics in Social Statistics
15. Communicating Statistical Results
Testing for Differences Between Means
One-Sample Tests
One-Sample Z-Test
Assumptions and Conditions
Test Statistic Calculation
Critical Values and P-Values
One-Sample t-Test
When to Use t vs. z
Assumptions
Degrees of Freedom
Interpreting Results
Two-Sample Tests
Independent Samples t-Test
Assumptions
Pooled Variance Approach
Separate Variance Approach
Levene's Test for Equality of Variances
Effect Size Measures
Welch's t-Test
When to Use
Advantages over Pooled t-Test
Mann-Whitney U Test
Non-parametric Alternative
Assumptions and Procedures
Paired-Samples Tests
Paired-Samples t-Test
When to Use
Assumptions
Calculating Difference Scores
Interpreting Results
Wilcoxon Signed-Rank Test
Non-parametric Alternative
Procedures and Interpretation
Analysis of Variance
One-Way ANOVA
Logic and Rationale
Between-Group Variance
Within-Group Variance
F-Statistic
Assumptions of ANOVA
Post-Hoc Comparisons
Tukey's HSD
Bonferroni Correction
Scheffe's Test
Two-Way ANOVA
Main Effects
Interaction Effects
Simple Effects Analysis
Interpreting Interaction Plots
Repeated Measures ANOVA
Within-Subjects Designs
Sphericity Assumption
Non-parametric Alternatives
Kruskal-Wallis Test
Friedman Test
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9. Hypothesis Testing
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11. Analysis of Categorical Data