# 数据分析与统计推断

This course introduces you to the discipline of statistics as a science of understanding and analyzing data. You will learn how to effectively make use of data in the face of uncertainty: how to collect data, how to analyze data, and how to use data to make inferences and conclusions about real world phenomena.

Dr. Mine Çetinkaya-Rundel

The goals of this course are as follows:

Recognize the importance of data collection, identify limitations in data collection methods, and determine how they affect the scope of inference.
Use statistical software (R) to summarize data numerically and visually, and to perform data analysis.
Have a conceptual understanding of the unified nature of statistical inference.
Apply estimation and testing methods (confidence intervals and hypothesis tests) to analyze single variables and the relationship between two variables in order to understand natural phenomena and make data-based decisions.
Model and investigate relationships between two or more variables within a regression framework.
Interpret results correctly, effectively, and in context without relying on statistical jargon.
Critique data-based claims and evaluate data-based decisions.
Complete a research project that employs simple statistical inference and modeling techniques.

Week 1: Unit 1 - Introduction to data
Part 1 – Designing studies
Part 2 – Exploratory data analysis
Part 3 – Introduction to inference via simulation
Week 2: Unit 2 - Probability and distributions
Part 1 – Defining probability
Part 2 – Conditional probability
Part 3 – Normal distribution
Part 4 – Binomial distribution
Week 3: Unit 3 - Foundations for inference
Part 1 – Variability in estimates and the Central Limit Theorem
Part 2 – Confidence intervals
Part 3 – Hypothesis tests
Week 4: Finish up Unit 3 + Midterm
Part 4 – Inference for other estimators
Part 5 - Decision errors, significance, and confidence
Week 5: Unit 4 - Inference for numerical variables
Part 1 – Comparing two means
Part 2 – Bootstrapping
Part 3 – Inference with the t-distribution
Part 4 – Comparing three or more means (ANOVA)
Week 6: Unit 5 - Inference for categorical variables
Part 1 – Single proportion
Part 2 – Comparing two proportions
Part 3 – Inference for proportions via simulation
Part 4 – Comparing three or more proportions (Chi-square)
Week 7: Unit 6 - Introduction to linear regression
Part 1 – Relationship between two numerical variables
Part 2 – Linear regression with a single predictor
Part 3 – Outliers in linear regression
Part 4 – Inference for linear regression
Week 8: Unit 7 - Multiple linear regression
Part 1 – Regression with multiple predictors
Part 2 – Inference for multiple linear regression
Part 3 – Model selection
Part 4 – Model diagnostics
Week 9: Review / catch-up week
Bayesian vs. frequentist inference
Week 10: Final exam

Basic math, no programming experience required. A genuine interest in data analysis is a plus!

Lectures are designed to be self-contained, but we recommend that students refer to the book OpenIntro Statistics (Second Edition). The course will closely follow this book, and hence the text can serve as supplementary material to the videos. In addition, practice problems will be assigned from the book. The book is open-source and freely available online at openintro.org.

The class will include video lectures, between 5 and 10 minutes in length, containing a few quiz questions per video. There will be homework assignments consisting of graded multiple choice quizzes and optional, ungraded questions from the textbook, computational data analysis assignments, a data analysis project, a midterm, and a final exam.

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