STAT 505: Applied Multivariate Statistical Analysis

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course overview

Students completing this course should be able to:

  • Select appropriate methods of multivariate data analysis, given multivariate data and study objectives;
  • Write SAS and/or Minitab programs to carry out multivariate data analyses;
  • Interpret results of multivariate data analyses.

course topics

This graduate level course covers the following topics:

  • Working with multivariate data and its graphical display
  • Measures of central tendency, variance and association of multivariate data
  • Interpreting the meaning of linear combination of random variables
  • Understanding the multivariate normal distribution and how it is used
  • Understanding the properties of sample mean vectors and correlation in multivariate data contexts
  • Understanding the role that partial correlation may play in multivariate contexts
  • Understanding how data reduction techniques can be used to generate more meaningful interpretation
  • Using principal component analysis
  • Using factor analysis
  • Using canonical correlation analysis
  • Using cluster analysis
  • Understanding the implications involved in making inferences in multivariate contexts
  • Using Hotelling's T-square in various multivariate contexts
  • Using discriminant analysis
  • Using MANOVA
  • Using repeated measures analysis

Here is a link to the Online Notes for STAT 505.


STAT 501 and STAT 502; Matrix Algebra (see Review).


Johnson, R.A., and Wichern, D.W. (2007). Applied Multivariate Statistical Analysis. 6th ed. Prentice Hall, New York.


SAS is the recommended software and shall be used for all in-class demonstrations of statistical analyses, homework assignments, and exams. See the Statisitical Software page for more information.

SAS will be supported and sample programs will be supplied but you will be required to do some programing on your own. Due to different software applications, software versions and platforms there may be issues with running code. Students must be proactive in seeking advice and help from appropriate sources including documentation resources, other students, the teaching assistant, instructor or helpdesk.

Statistical software SAS involves programming.  Students should already feel comfortable using SAS at a basic level, be a quick learner of software packages, or able to figure out how to do the required analyses in another package of their choice. 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 505.

assessment plan

  • Homework  - 35%
  • Exams - 65 %

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. Stephen Rathbun was the original author to develop materials for this course. Dr. Andrew Wiesner has added to and updated the focus of this course. Dr. Srabashi Basu and Dr. Scott Roths have recently adapted the online course materials for STAT 505.