STAT 461: Analysis of Variance

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course overview

At the end of this course, successful students will be able to

  1. Design and conduct an experiment that exhibits both a treatment design and randomization design that allow for the testing of differences between the levels of a single or multiple treatments of interest.
  2. Given a description of an experiment, correctly identify common design elements, including (a) Crossed factorial designs with interactions, (b) Nested factorial designs, (c) Blocking factors, (d) Nuisance variables, (e) Split-plot designs, (f) Repeated measures, and (g) Random effects.
  3. Specify an appropriate statistical model for observations resulting from a designed experiment exhibiting the elements in item 2.
  4. Identify estimable terms in a statistical model for an experiment, find the least squares estimator of estimable terms, and specify the statistical distribution of the estimator.
  5. Conduct and correctly interpret statistical hypothesis tests for the overall effect of a treatment and for the effects of contrasts.
  6. Correctly employ methods for multiple comparisons to control the experimentwise error rate when multiple hypothesis tests are conducted.
  7. Examine model assumptions using residual plots and a description of the experiment. Apply remedial measures such as transformations to the response when such transformations improve adherence to modeling assumptions.

course topics

  • Analysis of variance for single factor designs,
  • Analysis of variance for multifactor designs,and
  • Response surface methodology.


  • STAT 200, STAT 240, STAT 250, STAT 301 or STAT 401


A.Dean and D. Voss. (1999), Design and Analysis of Experiments. ISBN-13: 978-1475772920 (available for free download from the PSU Library website)

Applied Linear Statistical Models by Kutner, Nachtsheim, Neter, and Li, 5th Edition. (this text is recommended as a reference, but not required).


This course will use the statistical software program SAS. See the Statistical Software page for more information.

assessment plan

Homework: The homework will consist of problems selected from the textbook or given within the notes and will be listed in the Homework folder.

Participation: The class will have discussion boards and you will be expected to follow the discussion boards and also participate in any discussions. You are also expected to keep up with all class communications and check Canvas on a regular basis.

Mid-Terms: The Midterms will be timed. They are to be submitted similarly to the Homework.

Final Exam: The final exam will be comprehensive and proctored (please see your course syllabus you receive upon enrollment for details).

Project: students will be required to design, carry out, and analyze an experiment. This project can be done in small groups, and you are encouraged to begin thinking now about an experiment that you could undertake during the semester. Additional details will be given after the first midterm.

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. Ephraim Hanks is the primary author of these course materials.