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Statistics
Statistics with R
1. Introduction to R and Statistical Computing
2. R Fundamentals and Basic Operations
3. R Package System
4. R Data Structures
5. Data Import and Export
6. Data Cleaning and Preprocessing
7. Data Manipulation with dplyr
8. Descriptive Statistics
9. Data Visualization Fundamentals
10. Advanced Data Visualization with ggplot2
11. Probability Theory
12. Probability Distributions
13. Sampling and Sampling Distributions
14. Statistical Inference Foundations
15. Hypothesis Testing Framework
16. One-Sample Tests
17. Two-Sample Tests
18. Chi-squared Tests
19. Analysis of Variance (ANOVA)
20. Correlation Analysis
21. Simple Linear Regression
22. Regression Diagnostics
23. Multiple Linear Regression
24. Generalized Linear Models
25. Nonparametric Statistics
26. Introduction to Time Series Analysis
27. Introduction to Machine Learning
28. Reproducible Research
29. Statistical Computing Best Practices
15.
Hypothesis Testing Framework
15.1.
Hypothesis Testing Logic
15.1.1.
Scientific Method
15.1.2.
Statistical Hypotheses
15.1.3.
Null and Alternative Hypotheses
15.1.4.
One-tailed vs Two-tailed Tests
15.2.
Test Statistics
15.2.1.
Standardized Test Statistics
15.2.2.
Sampling Distribution Under Null
15.2.3.
Critical Values
15.3.
Decision Making
15.3.1.
Rejection Regions
15.3.2.
p-values
15.3.3.
Significance Levels
15.3.4.
Statistical vs Practical Significance
15.4.
Types of Errors
15.4.1.
Type I Error
15.4.2.
Type II Error
15.4.3.
Power of a Test
15.4.4.
Relationship Between Errors
15.5.
Steps in Hypothesis Testing
15.5.1.
State Hypotheses
15.5.2.
Choose Significance Level
15.5.3.
Select Test Statistic
15.5.4.
Determine Critical Value
15.5.5.
Calculate Test Statistic
15.5.6.
Make Decision
15.5.7.
Draw Conclusion
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14. Statistical Inference Foundations
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16. One-Sample Tests