STAT 504: Analysis of Discrete Data

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course overview

Course Objectives

  • To develop a critical approach to the analysis of contingency tables
  • To examine the basic ideas and methods of generalized linear models
  • To link logit and log-linear methods with generalized linear models
  • To develop basic facility in the analysis of discrete data using SAS/R

course topics

This graduate level course covers the following topics:

  • Quick review of discrete probability distributions: binomial, multinomial, and Poisson.
  • An introduction to the concept of likelihood.
  • Implementing tests for one-way tables using Pearsons X2 and likelihood-ratio G2 statistics.
  • Using contingency tables including 2 × 2 and r × c tables, tests for independence and homogeneity of proportions, Fishers exact test, odds ratio and logit, other measures of association.
  • Using 3-way tables in full independence and conditional independence contexts, collapsing and understanding Simpson's paradox.
  • Using generalized linear models in Poisson regression and logistic regression contexts for dichotomous response, including interpretation of coefficients, main effects and interactions, model selection, diagnostics, and assessing goodness of fit.
  • Using polytomous logit models for ordinal and nominal response.
  • Using loglinear models (and graphical models) for multi-way tables.
  • And other topics as time permits (and due to the interests).  These may include causality, repeated measures, generalized least squares, mixed models, latent-class models, missing data, and/or algebraic statistics approaches.

Here is a link to the Online Notes for STAT 504.


STAT460 or STAT461 or STAT502; Matrix Algebra (see Review). Basic knowledge of either SAS or R is strongly encouraged.


Agresti, A. (2013). Categorical Data Analysis, 3rd Edition, Wiley.

This is the new and improved text of Agresti (1996). It is less theoretical and therefore less technical than Agresti (2002). Students are free to purchase either 2007 or 2002 text for this course. References are provided in the lesson materials for both texts.


SAS (, and R ( are used in this course. See the Statistical Software page  for more information about acquiring a copy of these applications.

SAS and R will be supported. Sample programs will be supplied but students will be required to do some programing on their own. Students should already feel comfortable using either SAS or R, or be a quick learner of software packages, or be able to figure out how to do the required analyses in another package of their choice. Due to different software versions and platforms there may be issues with running a code. Students should NOT wait to the point of frustration but must be proactive in seeking advice and help from appropriate sources including documentation resources, other students via the online discussion boards, the teaching assistant, instructor or helpdesk.  Students who have no experience with programming or are anxious about being able to manipulate software code are strongly encouraged to take the one-credit courses in either SAS or R in order to establish this foundation before taking STAT 504.

assessment plan

The course syllabus that you receive at the beginning of the course will specify the number and weight of course assessments. In general, the grade in this course will be based upon the following allocations. 

  • Homework – 30%
  • 2 online, timed exams – a Midterm 20% – and a Final Exam 30%
  • Course Project – 20%

academic integrity

All Penn State policies regarding ethics and honorable behavior apply to this course. Academic integrity is the pursuit of scholarly activity free from fraud and deception and is an educational objective of this institution. All University policies regarding academic integrity apply to this course. Academic dishonesty includes, but is not limited to, cheating, plagiarizing, fabricating of information or citations, facilitating acts of academic dishonesty by others, having unauthorized possession of examinations, submitting work of another person or work previously used without informing the instructor, or tampering with the academic work of other students.

For any material or ideas obtained from other sources, such as the text or things you see on the web, in the library, etc., a source reference must be given. Direct quotes from any source must be identified as such.

All exam answers must be your own, and you must not provide any assistance to other students during exams. Any instances of academic dishonesty WILL be pursued under the University and Eberly College of Science regulations concerning academic integrity. For more information on academic integrity, see Penn State's statement on plagiarism and academic dishonesty.

The Eberly College of Science Code of Mutual Respect and Cooperation embodies the values that we hope our faculty, staff, and students possess and will endorse to make The Eberly College of Science a place where every individual feels respected and valued, as well as challenged and rewarded.


Penn State welcomes students with disabilities into the University's educational programs. If you have a disability-related need for reasonable academic adjustments in this course, contact the Office for Disability Services (ODS) at 814-863-1807 (V/TTY). For further information regarding ODS, please visit the Office for Disability Services Web site at

In order to receive consideration for course accommodations, you must contact ODS and provide documentation (see the documentation guidelines at If the documentation supports the need for academic adjustments, ODS will provide a letter identifying appropriate academic adjustments. Please share this letter and discuss the adjustments with your instructor as early in the course as possible. You must contact ODS and request academic adjustment letters at the beginning of each semester.

course author

Dr. Aleksandra Slavkovic is the primary author of these course materials and has taught this course for many semesters.