Statistical Inference Course Syllabus

Overview: This course provides a comprehensive introduction to statistical inference, covering core concepts and practical applications using R programming. Designed for learners with a basic background in statistics and R, it spans approximately 44 hours of content across five modules, combining video lectures, readings, quizzes, and hands-on programming assignments. The course is self-paced, allowing flexible learning while building a strong foundation in drawing conclusions from data.

Module 1: Probability & Expected Values

Estimated time: 18 hours

• Fundamentals of probability
• Random variables and probability mass functions
• Density functions and conditional probability
• Bayes’ rule and independence
• Expected values and their properties

Module 2: Variability, Distribution, & Asymptotics

Estimated time: 11 hours

• Measures of variability and distribution shapes
• Central Limit Theorem and asymptotic behavior
• Confidence intervals and sampling distributions
• Normal approximation and its applications

Module 3: Intervals, Testing, & P-values

Estimated time: 8 hours

• Construction and interpretation of confidence intervals
• Hypothesis testing framework
• Understanding and calculating p-values
• Type I and Type II errors

Module 4: Power, Bootstrapping, & Permutation Tests

Estimated time: 7 hours

• Statistical power and its determinants
• Bootstrapping techniques for estimating uncertainty
• Permutation tests for hypothesis testing

Prerequisites

• Basic understanding of statistics (e.g., mean, standard deviation, probability)
• Familiarity with R programming language
• Completion of introductory statistics or data science coursework recommended

What You'll Be Able to Do After

• Understand the process of drawing conclusions about populations from data
• Describe variability, distributions, limits, and confidence intervals
• Use p-values, confidence intervals, and permutation tests effectively
• Make informed decisions in data analysis using statistical inference methods
• Apply bootstrapping and hypothesis testing techniques in real-world scenarios