PSY 626: Bayesian Statistics for Psychological Science

Fall 2025
Days/times: Tuesday, Thursday / 12:00 pm - 1:15 pm
Location: PRCE 255

Instructor:

Name	Office	Email	Phone	Office hours
Greg Francis	PSYCH 3186	gfrancis@purdue.edu	494-6934	MWF 1:00 - 2:00 pm

Materials (lectures, readings, datasets, code):

This material can be downloaded from the class website at http://www2.psych.purdue.edu/~gfrancis/Classes/PSY626/indexF25.html

• Efect sizes, power, and violations of hypothesis testing. PPT slides for Lecture 1, Francis (2019).
• Replication and hypothesis testing. PPT slides for Lecture 2, Francis (2012).
• Publication bias. PPT slides for Lecture 3, Francis (2014).
• Prediction and comparing models. PPT slides for Lecture 4.
• Shrinkage. PPT slides for Lecture 5, Shrinkage.R, ShrinkagePrediction.R.
• Bayesian linear regression
• PPT slides for Lecture 6, VisualSearch.csv, VisualSearch.R.
• PPT slides for Lecture 7, VisualSearch2.R, VisualSearch3.R.
• Information criterion. PPT slides for Lecture 8, VisualSearch4.R.

Text:

McElreath, R Statistical Rethinking: A Bayesian Course with Examples in R and Stan. Try to get the second edition. Ordering information and code examples are at the book web site.

In case you do not yet have the textbook, Chapters 1 and 2 of the textbook are on-line.

As mentioned in class, you might want to install the rethinking package on your own computer. Here is some guidance for a modern Mac (note the dependencies near the top).

General guidance is at the rethinking GitHub. Note, you cannot get by with just the slim install because we will soon need the MCMC algorithms.

There is an R script that might help, but I think you still need to first install a C-compiler.

General plan: The course will explain why you might want to use Bayesian methods instead of frequentist methods (such as t-tests, ANOVA, or regression). The general plan is to:

1. Explain some problems/difficulties with frequentist methods: Publication bias, optional stopping, questionable research practices.
2. Discuss differences between hypothesis testing and prediction: mean squared error, shrinkage.
3. Discuss methods for prediction: likelihood, AIC, BIC, cross-validation.
4. Explain the basic ideas of Bayesian methods: non-informative priors, informative priors.
5. Provide hands-on examples of applying Bayesian methods: Bayes Factors, hierarchical models.

Throughout, we will be using computer programs to demonstrate the ideas. There will not be any proofs.

Class home page: The home page for this course is http://www.psych.purdue.edu/~gfrancis/Classes/PSY626/indexF25.html From this page you can download lecture notes, view the class schedule, view current grades, and connect to the various homework assignments.

Homework: Assignments will be due approximately every two weeks. The intention is to use the homework assignments as a way of practicing the concepts we discuss in class. They will be graded, but only to insure that students actively participate.

1. Homework 1 (due September 2): as PDF, as MS Word, Calculators at IntroStats Online
2. Homework 2 (due September 12): as PDF, as MS Word, ComputePower.R

Project: In the last two weeks, students will present a Bayesian (or related) analysis of some of their own data. If you do not happen to have a data set, we will get one for you. There is no formal requirement for what to include in the project, but here's a few thoughts.

Assumed background:

• It would be nice, but not necessary, if you had some previous exposure to calculus.
• Doing any kind of Bayesian analysis requires some programming. We will be using the free R software. Many people like the R studio programm, but the default interface will also work. You do not need to be an expert programmer, but if you have little programming experience, you will have some catching up to do.
• Students should have experience with typical statistical methods (t-test, ANOVA, regression).