Introduction to Statistics


Shravan Vasishth.


The course takes the participants through the basic theory of frequentist statistics: random variables, the sampling distribution, Type I, II, S, M errors, t-tests, linear models, and linear mixed models.


I am assuming that the students have used R and have done some data analysis using R.

Please install the following software before coming to the course

We will be using R, and RStudio, so make sure you install these on your computer.


After completing this course, the participant will have become familiar with the basic ideas behind frequentist methods. They will be able to carry out and interpret the results of the following statistical tests: t-tests, hypothesis tests using linear models and linear mixed models.

Course materials

You can either download the slides and exercises from the links below, or click here to download everything in one shot as a zip archive. If you use github, you can clone this repository:

Schedule and slides + exercises

Further details are available on the Moodle website. Here we provide only the video lectures.
  1. Developing the right mindset for statistics:
  2. Introduction to the course
  3. Some foundational ideas
  4. The sampling distribution of means
  5. Type I, II error
  6. Some subtleties associated with the humble t-test:
  7. Introduction to linear models (and the connection to t-tests):
  8. OPTIONAL, somewhat technical lecture: The matrix formulation of the linear model, the likelihood ratio test, ANOVA:

  9. Contrast coding:
  10. Linear mixed models:

  11. Generalized linear models:
  12. Simulating data:
  13. Developing a reproducible workflow:

Additional readings

R programming
  1. Getting started with R
  2. R for data science
  3. Efficient R programming.
Further reading (articles)
  1. Shravan Vasishth and Bruno Nicenboim. Statistical Methods for Linguistic Research: Foundational Ideas – Part I. Language and Linguistics Compass, 10(8):349-369, 2016.
  2. Daniel J. Schad, Sven Hohenstein, Shravan Vasishth, and Reinhold Kliegl. How to capitalize on a priori contrasts in linear (mixed) models: A tutorial. Submitted, 2019.
  3. Barr, D. J., Levy, R., Scheepers, C., & Tily, H. J. (2013). Random effects structure for confirmatory hypothesis testing: Keep it maximal. Journal of memory and language, 68(3), 255-278.
  4. Bates, D., Kliegl, R., Vasishth, S., & Baayen, H. (2015). Parsimonious mixed models. arXiv preprint arXiv:1506.04967.
  5. Hannes Matuschek, Reinhold Kliegl, Shravan Vasishth, R. Harald Baayen, and Douglas Bates. Balancing Type I Error and Power in Linear Mixed Models. Journal of Memory and Language, 94:305-315, 2017.