Language and Computation foundational course:
The Foundations of Statistics: A Simulation-Based Approach.
I will develop the statistical theory underlying hypothesis testing from first principles, using elementary probability theory and Monte Carlo simulations. I will use the programming language R (http://cran.r-project.org/). In addition, we will discuss issues such as data visualization and data management for realistic datasets.
We will use a newer version of this freely available online textbook: http://www.ling.uni-potsdam.de/~vasishth/SFLS.html
Day 1: Basics of R
Day 2: t-tests and confidence intervals
Day 3: statistical power, Type I and Type II errors
Day 4: linear models and their connection with t-tests
Day 5: multiple regression and mixed-effects models
This course will be useful for anyone doing any kind of quantitative research. Students typically learn cookbook statistics, an approach which often leads to significant misunderstandings regarding hypothesis testing. This course has been developed to help correct such problems.
Each lecture will be accompanied by practical exercises to be completed after class; solutions will be provided the following day.