Description

About Stat 135 (Concepts of Statistics)

This is one of the three foundational courses of the Statistics Major, the other two being Stat 134 (Concepts of Probability) and Stat 133 (Concepts of Computing). While Stat 134, which is a serious prerequisite for Stat 135, is a course in probability, Stat 135 is a course in statistical inference. It is a comprehensive survey course in statistical theory and methodology. Topics include parameter estimation, hypothesis testing, statistical tests (parametric and non parametric) and linear regression (single and an example of multiple). We will cover most of the content of chapters 7 through 14 in the text Mathematical Statistics and Data Analysis by John Rice (3rd Edition), with a brief look at the content in chapters 5 and 6.

Learning Goals

By the end of the semester, you should be able to:

  1. Clearly interpret point estimates, confidence intervals, and hypothesis tests for an audience without statistical training.
  2. Construct common estimators, statistical tests and confidence interval procedures using probability theory.
  3. Evaluate the relative strengths and limitations of several estimation or inference procedures for the same problem using mathematical concepts including unbiasedness, efficiency, and power.
  4. Recommend an approach and carry out estimation and inference for canonical statistics problems including tests of association between two variables and fitting probability distributions to univariate data.

Prerequisites

  • STAT 134 or an equivalent course in probability theory. Do NOT take 134 and 135 concurrently!!
  • Multivariable calculus, especially Lagrange multipliers.
  • Familiarity with moment-generating functions.
  • Familiarity with basic R concepts equivalent to the first ~6 weeks of Stat 133. Note that assignments involving computing must be completed in R.
  • Familiarity with linear algebra (matrix operations, inverses, and eigenvalues) for chapter 14.

Useful Textbooks

  • Mathematical Statistics and Data Analysis (3rd Edition), by John Rice: This is the main text that we will follow, and exercises will mostly be from here. Make sure that you have the third edition.
  • R for Data Science, by Hadley Wickham, Mine Çetinkaya-Rundel, and Garrett Grolemund
  • Statistics, by Freedman, Pisani, and Purves: This is the text for Stat 2. It has no coding, but nevertheless is a wonderful book to read, and I strongly recommend reading through it to improve your understanding of statistics.
  • Veridical Data Science, by Bin Yu and Rebecca Barter: This is a new book written by Prof. Yu and R. Barter and introduces a framework to practice data science. Though it doesn’t really talk about statistical inference, which is the focus of our class, it discusses how to apply the methods to get reproducible and trustworthy results.
  • Stat Labs, by Deborah Nolan and Terry Speed: Statistical topics are introduced via case studies.

As we progress through the course, I may add more books to this list.