COURSE: STA 6707 (Sections 2096 and 2097) Multivariate Methods
Class Meetings: MW 4:00-5:15 PM
TEXTBOOK: Applied Multivariate Statistical Analysis, 6th edition by Johnson &
Wichern. Published by Perason/Prentice Hall.
TESTING PROCEDURES
Regular homework assignments are given to supplement the lectures and
Text book. Grades will be determined based on performance in all categories below. The
midterm exams are open book, but no formula sheets exams. The final exam is
comprehensive and is has a take-home portion.
Group Assignments
Exam I:
Exam II:
Final Exam:
5%
30%
30%
35%
I have modified the syllabus to reflect allowed group work on all assignments. I will ask
you to use student mentoring as a method for learning the course material. There is a 5%
weight given for individual assignments, but each group of students works together on
assignments. I will collect assignments, and I will post the solutions by some of the
groups who seem to be doing very well in their homework.
Discussions: It is very important that each student contributes to the class lectures by
discussions and by active participation throughout the semester
SAS: While it is allowed to use any software package for basic data set cleaning and
arranging, I expect students to use SAS for the inferential portions once we cover
MANOVA. Matrix manipulations may be done with any software package. If you have
never had any experience with SAS, start early in the course learning it.
COURSE OUTLINE
Multivariate extensions of Chi-Square and t-tests, discrimination and classification
procedures, application to diagnostic problems in biological, medical, anthropological
and social research: multivariate analysis of variance,; factor analysis and principal
components analysis. Prerequisites: STA 5206 or STA 5207. It helps if you have some
linear algebra background on matrices and eigenvalues.
Researchers in the social, biological, and physical sciences frequently collect
measurements on several variables that are related. In this course we will cover statistical
methods for describing and analyzing these multivariate data. Data analysis becomes
truly fascinating and challenging when we go beyond one variable and involve several
variables. A solid statistical background will help a lot in this course. This is not a
number crunching course.
Objectives:
1. To develop methods for use in the analysis of multivariate data.
2. To illustrate this methodology by using case studies.
Background: This course is taught to graduate students who have already covered at
least on graduate course in statistics. If you already have had STA 5206
and STA 5207 then you should be well prepared for taking this course.
The material is very useful for applications and for giving students a
broader understanding of statistics. Psychology students (in particular)
would benefit greatly from topics such as Factor Analysis and Principal
Components Analysis. Mathematics and Statistics majors will benefit
from linear algebra and eigenvalue decomposition.
Outline:
I will attempt to cover most of the topics that are listed below, and we
will be able to cover some of them as projects done by the students.
1. Aspects of Multivariate Analysis.
2. An introduction to Matrices and Random Samples.
3. The Multivariate Normal Distribution.
4. Multivariate Tests of Hypotheses.
5. Multivariate Analysis of Variance.
6. Principal Components Analysis.
7. Factor Analysis.
Expected Student Outcomes:
Students will be able to perform multivariate tests for the one sample case.
Students will be able to perform multivariate tests for paired data.
Students will be able to perform multivariate tests for two samples or more.
Students will be able to perform a factor analysis.
Students will be able to perform a principal components analysis.
Discussions: It is very important that each student contributes to the class lectures by
discussions and active participation throughout the semester.
Homework:
Students are required to attempt all assigned homework problems. It is
allowed to work together, but there should be no copying of answers.
SAS:
There will be a need to use some computer software to evaluate matrix
algebra, and we will definitely use SAS for Factor Analysis and Principal
Components Analysis and MANOVA.
Selected References:
Go to the library and check out a text on multivariate. There are several newer books out.
"Classics" :
1. Morrison, D. F. (1976), Multivariate Statistical Methods.
2. Harris, R. J. (1974), A Primer of Multivariate Analysis.
3. Press, S. J. (1972), Applied Multivariate Analysis.
4. Tatsuoka, M.M. (1971), Multivariate Analysis: Techniques for Educational and
Psychological Research.
5. Bennet, S. and Bowers, D. (1976), An Introduction to Multivariate Techniques for
Social and Behavioral Sciences.
6. Everitt, B. (1978), Graphical Techniques for Multivariate Data.
7. Maxwell, A. E. (1977), Multivariate Analysis in Behavioral Research.
8. Overall, J. E. and Klett, C. J. (1972), Applied Multivariate Analysis.
9. Miller, K. S. (1975), Multivariate Distributions.
10. Harman, H. R. (1967), Modern Factor Analysis.
11. Pillai, K. C. S. (1960), Statistical Tables for Tests of Multivariate Distributions.
12. Johnson, n. l. and Kotz, S. (1972), Distns. in Statistics: Continuous Multivariate
Distributions.
Resources: Make use of technology and online resources to obtain the latest resources on
multivariate methods. In particular, STATLINK is an international online group that
shares lecture notes and software on many topics in statistics. I have posted here the links
that are related to multivariate methods. You can use CTRL CLICK with the mouse to
access any of the links below.
General
Lecture notes on Multivariate Data Analysis by Nick Fieller -Multivariate Data Summary and
Hypothesis Testing, Dimensionality Reduction Techniques and Exercises -272 pagesMultivariate Analysis Lecture notes by J. D. Tubbs -Profile Analysis, PCA, Factor Analysis,
Discrimination Analysis, Cluster Analysis -234 pagesApplied Multivariate Statistical Analysis, by W.Hardle & L.SImar -488 pages- BOOK!
Multivariate Analysis (Statistical Inference for Astronomers), by T.Krishnan -60 pagesMultivariate Statistical Analysis by Philip B. Ender (on-line lecture notes) -Discriminant Analysis,
MANOVA, Factor AnalysisA Practical Guide to the Use of Selected Multivariate Statistics (on-line text) by Mike Wulder
Canonical Correlation Analysis by Hair, Black, Babin, Anderson and Tatham -29 pages-
Pattern Recognition and Intelligent Sensor Machines lecture notes by Texas A&M University
A Combinatorial Introduction to Cluster Analysis by Melvin F. Janowitz -46 pagesLecture notes on Multivariate Data Analysis by Ioannis Ntzoufras -Principal Component Analysis,
Factor Analysis, Discriminant Analysis, Clustering, MANOVA, -186 pages in Greek-
Factor Analysis
Lecture notes on Factor Analysis I by Elizabeth Garrett-Mayer -56 pagesLecture notes on Factor Analysis II by Elizabeth Garrett-Mayer -21 pagesFactor Analysis by Peter Tryfos -22 pagesFactor Analysis by Richard B. Darlington -on line lecture notesFactor Analysis by Geurt Jongbloed -17 pagesUnderatanding Factor Analysis by R.J. Rummel -on-line textbookIntroduction to Factor Analysis by Charles E. Reese and C. H. Lochmüller -on-line lecture notesExploratory Factor Analysis by Ledyard R. Tucker and Robert C. McCallum -General Concepts,
Extraction Techniques, Transformations -459 pages-
Principal Component Analysis
Lecture notes on Principal Component Analysis by A. James Schwab -69 slidesLecture notes on Principal Component Analysis: Validation, Outliers, and Reliability by A. James
Schwab -128 slidesA -very intuitive- Tutorial on Principal Component Analysis (Jonathon Shlens) - 13 pagesTutorial on Principal Compontent Analysis by Javier R. Movellan -9 pagesPrincipal Component Analysis by George Bebis -8 pagesPrincipal Component Analysis by Peter Tino -17 pagesA tutorial on Pricipal Component Analysis by Lindsay I. Smith -27 pages-
Discriminant Analysis
Discriminant Analysis Basic Relationships: Scores, Classification Accuracy by A. James Schwab
-122 slides-
Lecture notes on Discriminant Analysis by A. James Schwab -Outliers, Multicollinearity,
Validation -87 slidesDiscriminant Analysis by Daniel Peña Sánchez de Rivera -34 pagesDiscriminant Analysis -15 pagesLinear Discriminant Analysis- a Brief Tutorial by S. Balakrishnama and A. Ganapathiraju -9
pagesFisher Linear Discriminant Analysis by Max Welling -5 pagesHigh Dimensional Discriminant Analysis by Charles Bouveyron (joint work with S. Girard and C.
Schmid) -43 pagesFlexible Discriminant Analysis by Jerome Callut -17 pagesDiscrimination and Classification by Kritikou Katerina, Nikaki Katerina and Nikolaidou Chrysa -47
pages-
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Frequently Asked Questions
Must I attend all lectures during the announced lecturing times live? This is an
“online course” after all.  Yes, all students must do their best to attend almost
every lecture live. This is a very important requirement for student learning in the
graduate program at the Department of Mathematics and Statistics.
What does a “proctored exam” mean?  The exam will be taken at an approved
educational center that you choose, and you will be proctored (overlooked) as you
take the exam. There may be a fee included, depending on the center doing the
proctoring. You must submit to the appropriate drop box on e-learning the proctor
information. UWF has a special form for proctor information with guidelines.
May I use my relative or spouse as my proctor for exams?  No, this would be
unacceptable. Always start by looking for a junior college close to where you live.
I am an officer in the US military. How would I take proctored exams?  A
higher ranked officer may be used as your proctor. Many military bases have
educational centers that can be used for proctoring.
I am stationed in Japan at a U.S. military base. The time difference is
considerable. How will I be able to attend lecture live and when will I take my
proctored exams?  I am flexible in such situations, and we will work out how
you will go through this online course. Exams can be taken at times that are
manageable for you at your local time.
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How will I submit my exams to you?  I will send your proctor the exam in a
timely fashion, and she/he will email me back your completed exam after
scanning it at the educational center where you will be taking the exam.
Do I have multiple options when to take the proctored exam?  All exams will
be taken on specific days that I will announce in class and on e-learning. There is
flexibility at what time on a given day you can take the exam, as long as the
proctor will be able to email me back your scanned completed exam on the same
day.
I travel a lot, and I need to take my exams on weekends. Is this possible?  No,
this is not possible since all students must take the exams on the same day.
How do I send you my assignments when I complete them?  You will be able
tow rite up each assignment with pencil and paper, followed by scanning it to a
single PDF file with maximum file size 2MB. Then you will submit that (single
PDF) file to the appropriate drop box on e-learning.
Can you give me some tips on how to scan the assignments?  There is a file
posted on e-learning on how to scan assignments.
Must I participate in e-learning discussions?  Your active participation on elearning with questions and answers and tips for assignments is extremely
valuable to all students and to your better student learning of the course material.
May I send you emails on the course material throughout the semester?  I have
many students enrolled in my classes each semester, and it is most efficient to
limit emails to personal issues that you do not want to post on e-learning.
Whatever I address on e-learning will stay posted for an entire semester, and all
students will benefit from my input there.
May I drop the course any time during the semester?  Always check with the
announced UWF deadlines for dropping courses without penalties. There is no
“late W” assigned by me. It is your responsibility to keep track of deadlines.
May I leave the class room when I do not want to complete attending a lecture?
 While it is naturally allowed to leave the class room to go to the restroom or if
you should not feel well, it is disrupting the lecture if a student leaves the class
room for no justifiable reasons. If you know before the lecture starts that you must
leave early, just inform me about it at the start of the lecture. Then it is fine to
leave early.