STAT 350: Introduction to Statistics
Orientation
Course Introduction & Overview
Why Statistics? Why Now?
Course Roadmap
A Clear Note on Using AI
Getting Started: A Checklist
Homework Assignments on Edfinity
Miscellaneous Tips
Chapters
1. Introduction to Statistics
1.1. What Is Statistics?
1.2. Probability & Statistical Inference: How Are They Associated?
2. Graphical Summaries
2.1. Data Set Structure and Variable Types
2.2. Tools for Categorical (Qualitative) Data
2.3. Tools for Numerical (Quantitative) Data
2.4. Exploring Quantitative Distributions: Modality, Shape & Outliers
3. Numerical Summaries
3.1. Introduction to Numerical Summaries: Notation and Terminology
3.2. Measures of Central Tendency
3.3. Measures of Variability - Range, Variance, and Standard Deviation
3.4. Measures of Variability - Interquartile Range and Five-Number Summary
3.5. Choosing the Right Measure & Comparing Measures Across Data Sets
4. Probability
4.1. Basic Set Theory
4.2. Probability
4.3. Conditional Probability
4.4. Law of Total Probability and Bayes’ Rule
4.5. Bayesian Updating: Sequential Learning
4.6. Independence of Events
5. Discrete Distributions
5.1. Discrete Random Variables and Probability Mass Distributions
5.2. Joint Probability Mass Functions
5.3. Expected Value of a Discrete Random Variable
5.4. Varianace of a Discrete Random Variable
5.5. Covariance of Dependent Random Variables
5.6. The Binomial Distribution
5.7. Poisson Distribution
6. Continuous Distributions
6.1. Continuous Random Variables and Probability Density Functions
6.2. Expected Value and Variance of Continuous Random Variables
6.3. Cumulative Distribution Functions
6.4. Normal Distribution
6.5. Uniform Distribution
6.6. Exponential Distribution
7. Sampling Distributions
7.1. Statistics and Sampling Distributions
7.2. Sampling Distribution for the Sample Mean
7.3. The Central Limit Theorem (CLT)
7.4. Discrete Random Variables and the CLT
8. Experimental Design
8.1. Experimental and Sampling Designs
8.2. Experimental Design Principles
8.3. Basic Types of Experimental Design
8.4. Addressing Potential Flaws in Experimental Design
8.5. Examples of Experimental Design
8.6. Sampling Design
8.7. Sampling Bias
9. Confidence Intervals and Bounds
9.1. Introduction to Statistical Inference
9.2. Confidence Intervals for the Population Mean, When σ is Known
9.3. Precision of a Confidence Interval and Sample Size Calculation
9.4. Confidence Bounds for the Poulation Mean When σ is Known
9.5. Confidence Intervals and Bounds When σ is Unknown
10. Hypothesis Testing
10.1. Type I Error, Type II Error, and Power
10.2. Hypothesis Test for the Population Mean When σ is Known
10.3. Hypothesis Test for the Population Mean When σ Is Unknown
10.4. P-values, Statistical Significance, and Formal Conclusion
11. Two Sample Procedures
11.1. Confidence Interval/Bound and Hypothesis Test for Two Samples
11.2. Comparing the Means of Two Independent Populations - Population Variances Are Known
11.3. Comparing the Means of Two Independent Populations - Pooled Variance Estimator
11.4. Comparing the Means of Two Independent Populations - No Equal Variance Assumption
11.5. Analyzing the Mean of Paired Differences Between two Dependent Populations
12. ANOVA
12.1. Introduction to One-Way ANOVA
12.2. Different Sources of Variability in an ANOVA Model
12.3. One-Way ANOVA F-Test and Its Relationship to Two-Sample t-Tests
12.4. Multiple Comparison Procedures and Family-Wise Error Rates
13. Simple Linear Regression
13.1. Introduction to Linear Regression: Correlation and Scatter Plots
13.2. Simple Linear Regression
13.3. Model Diagnostics and Statistical Inference
13.4. Prediction, Robustness, and Applied Examples
STAT 350: Introduction to Statistics
12.
ANOVA
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12.
ANOVA
12.1. Introduction to One-Way ANOVA
12.2. Different Sources of Variability in an ANOVA Model
12.3. One-Way ANOVA F-Test and Its Relationship to Two-Sample t-Tests
12.4. Multiple Comparison Procedures and Family-Wise Error Rates