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Statistics
Statistics
1. Introduction to Statistics
2. Data Collection and Sampling
3. Descriptive Statistics: Organizing and Summarizing Data
4. Probability Theory
5. Probability Distributions
6. Sampling Distributions
7. Inferential Statistics: Estimation
8. Inferential Statistics: Hypothesis Testing
9. Analysis of Variance (ANOVA)
10. Correlation and Regression
11. Chi-Square Tests
12. Non-Parametric Statistics
13. Experimental Design
14. Advanced Topics in Statistics
Chi-Square Tests
Chi-Square Distribution
Degrees of Freedom
Goodness-of-Fit Test
Purpose
Testing Distributional Assumptions
Comparing Observed vs. Expected
Hypotheses
Null Hypothesis
Alternative Hypothesis
Test Statistic
Chi-Square Formula
Expected Frequency Calculation
Assumptions
Expected Frequency Requirements
Independence
Calculation Steps
Interpretation
P-value Approach
Critical Value Approach
Test for Independence
Purpose
Testing Relationship Between Variables
Contingency Table Analysis
Contingency Tables
Row and Column Variables
Cell Frequencies
Marginal Totals
Hypotheses
Independence Assumption
Expected Frequency Calculation
Formula
Degrees of Freedom
Test Statistic Calculation
Interpretation
Association Strength
Cramér's V
Test for Homogeneity
Purpose
Comparing Distributions
Multiple Populations
Hypotheses
Calculation
Similar to Independence Test
Different Interpretation
Interpretation
Population Differences
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12. Non-Parametric Statistics