Statistics
Courses
- Statistics 1
- Statistics 2
- 1. Sampling Distributions I: Random Sampling, Sampling Distributions, and Standard Error
- 2. Sampling Distributions II: Central Limit Theorem for the Sample Mean and Normal Approximation
- 3. Sampling Distributions III: \(\chi^2\), \(t\), and \(F\) Under Normal Theory for \(S^2\), \(\mu\), and \(\sigma_1^2/\sigma_2^2\) with Q–Q Diagnostics
- 4. Estimation I: Confidence Intervals for the Population Mean \(\mu\) (Known \(\sigma\) and Unknown \(\sigma\))
- 5. Estimation II: Confidence Intervals for Mean Differences \(\Delta=\mu_1-\mu_2\) and \(\mu_D\) (Pooled-\(t\), Welch-\(t\), and Paired-\(t\))
- 6. Estimation III: Confidence Intervals for \(p\), \(\sigma^2\) (via \(\chi^2\)), and \(\sigma_1^2/\sigma_2^2\) (via \(F\)) with Large-Sample Conditions
- 7. Estimation IV: Prediction Intervals for a Future Outcome \(x_0\) and Tolerance Intervals for Content \(p\) with Confidence \(1-\gamma\) (Specs \(\text{LSL}/\text{USL}\))
- 8. Hypothesis Testing I: Decision Framework, Type I/II Errors, P-Values, CI–Test Equivalence, and Power
- 9. Hypothesis Testing II: One-Sample Tests for \(\mu\), \(p\), and \(\sigma^2\)
- 10. Hypothesis Testing III: Two-Sample Tests for Differences in Means, Proportions, and Variability
- 11. Hypothesis Testing IV: Chi-Square Tests for Goodness-of-Fit and Independence in Contingency Tables
- 12. ANOVA I: Inference for Multiple Means via Variance Partition and the F Test
- 13. ANOVA II: Mean Comparisons with Blocks and Two-Factor Designs (Randomized Blocks and Two-Way ANOVA)
- 14. Correlation and Regression Readiness I: Covariance \(\sigma_{XY}\), Correlation \(\rho\), and Diagnostics for Linear Modeling (\(\beta_1\))
- 15. Regression and Correlation II: Simple Linear Regression (SLR) for Mean Response, Inference, and Prediction
- 16. Regression and Correlation III: Multiple Linear Regression (MLR) — Partial Effects, Indicators, and Collinearity
- 17. Regression and Correlation IV: Diagnostics, Influence, and Model Reporting