STAT 502: Analysis of Variance and Design of Experiments

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course overview

This is a graduate level course in analysis of variance (ANOVA), including randomization and blocking, single and multiple factor designs, crossed and nested factors, quantitative and qualitative factors, random and fixed effects, split plot and repeated measures designs, crossover designs and analysis of covariance (ANCOVA). This course is cohort-based, which means that there is an established start and end date, and that you will interact with other students throughout the course.

course topics

This is a course and analysis of variance (ANOVA), including randomization and blocking, single and multiple factor designs, crossed and nested factors, quantitative and qualitative factors, random and fixed effects, split plot and repeated measures designs crossover designs and analysis of covariance (ANCOVA).

This graduate level course covers the following topics:

  • Understanding the contexts in which ANOVA is appropriate
  • Using the notation and formulas used to compute values fundamental to ANOVA
  • Understanding the statistical model for analysis of variance and the relationship between ANOVA and regression
  • How to implement single factor or One-way ANOVA analyses
  • How to implement multiple factor ANOVA analyses
  • Extending treatment designs to include random effects
  • Understanding the importance that experimental design and randomization has in being able to interpret results
  • Understanding the structure of split-plot ANOVA designs and analysis
  • How to include a continuous covariate variable in ANOVA (ANCOVA)
  • Understanding the use of the General Linear Model
  • Fitting and testing polynomial models for a quantitative factor
  • Recognizing and analyzing repeated measures designs
  • Recognizing and analyzing cross-over repeated measures designs

Here is a link to the Online Notes for STAT 502.


STAT 501, Basic knowledge of Minitab and SAS is recommended.


There are two options of textbooks for this course. Students may use either:

The larger Applied Linear Statistical Models by Kutner, Nachtsheim, and Neter (5th edition) OR the smaller Analysis of Variance, a custom printing of the second half of the larger text (ISBN-97811216693-76).

Students may use either textbook listed.

The first half of the larger Applied Linear Statistical Models contains sections on regression models, the second half on analysis of variance and experimental design. The first 12 chapters on regression models are not covered in STAT 502, however these topics are covered in STAT 501 where these chapters are required. Students may consider purchasing the larger text if they are taking both courses. Applied Linear Statistical Models is considered to be one of the "bibles" of applied statistics so it probably will have value to you beyond this course.


Students will use both SAS and Minitab. If you are taking additional upper level STAT courses we recommend that you purchase a permanent license for Minitab. See the Statisitical Software page for more information about accessing these applications.  PLEASE NOTE: The Minitab v. 14 Student Version does not have full statistical functionality and is not recommended for STAT courses.

Minitab and SAS 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 Minitab and SAS, 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 course in SAS in order to establish this foundation before taking STAT 502.

assessment plan

  • Homework - There will be a homework assignment for each lesson.
  • Exams - There will be three exams. You will need to use your book to access the tables in the back.These exams will be proctored.
  • Project - each student will find an interesting ANOVA data set from his or her own area of application, analyze it and write a report on it. It must have at least 3 pages of discussion, not just a statement of results.

PLEASE NOTE: This course may require you to take exams using certain proctoring software that uses your computer's webcam or other technology to monitor and/or record your activity during exams. The proctoring software may be listening to you, monitoring your computer screen, and viewing you and your surroundings. By enrolling in this course, you consent to the use of the proctoring software selected by your instructor, including but not limited to any audio and/or visual monitoring which may be recorded. (Read more...)

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. Durland Shumway is the author of these course materials and has taught this course for many semesters in residence and more recently online.