Education | Multivariate Analysis in Educational Research
Y604 | 5991 | Dr. Ginette Delandshere


Students enrolled in the course should have completed Y502 or its
equivalent [Y603 also recommended].  Students should also have prior
knowledge of a computer system for accessing SAS or SPSS software or
have experience with their WINDOWS applications.

Course Content

This course is based on the premise that the function of statistics
is to formulate arguments for explaining comparative differences and
relationships in data.  This course focuses on the General Linear
Model (GLM) and the various forms it takes in the multivariate
context.  The forms of the model will be discussed in relationship to
the particular research questions for which they are appropriate.  A
range of multivariate statistical analysis procedures are considered
to examine relationships between multiple variables (e.g., multiple
dependent and/or independent variables) and comparisons will be made
to their univariate equivalent.  Principal component and factor
analysis will also be covered as a way to reduce the number of
measured variables to a smaller number of scores or underlying

Confirmatory factor analysis and the testing of simple structural
models will also be introduced as well as structural equation
modeling which allows for the examination of multiple relationships
among variables and for taking into account measurement error (using
measurement models for latent variables).

The limitations (i.e., assumptions) and unresolved issues of each
forms of the GLM will be examined.  Students will learn to formulate
research questions, to select appropriate analysis procedures, to
conduct statistical analyses, and to report, interpret and write up
narratives of the results in relation to the research questions and


1.To understand the nature and function of multivariate statistics
and to use appropriate procedures to answer specific research

2.To carry out statistical analyses and to verify the underlying

3.To interpret computer printouts, report and write up results in
relation to specific research contexts.


Two sets of textbooks have been ordered for this course and you can
work from either set depending to your preference.  Set 1 includes
the Sage Publication series that cover the material for this course.
Set 2 is a comprehensive textbook.  Notes are also made available for
each class session on Oncourse:

Set 1

Namboodiri, K.  Matrix Algebra, An Introduction #38, Beverly Hills,
CA: Sage Publications, Inc.

Lewis-Beck, M.S. (1980).  Applied Regression, An Introduction #22,
Beverly Hills, CA: Sage Publications, Inc.

Berry, W.D. & Feldman, S. (1985).  Multiple Regression in Practice
#50, Beverly Hills, CA: Sage Publications, Inc.

Bray, J.H. & Maxwell, S.E. (1985).  Multivariate Analysis of Variance
#54, Beverly Hills, CA: Sage Publications, Inc.

Klecka, W.R. (1980).  Discriminant Analysis #19, Beverly Hills, CA:
Sage Publications, Inc.

Kim, J-O. & Mueller, C. W. (1978).  Introduction to Factor Analysis
#13, Beverly Hills, CA: Sage Publications, Inc.

Kim, J-O. & Mueller, C. W. (1978).  Factor Analysis:  Statistical
Methods and Practical Issues #14, Beverly Hills, CA: Sage
Publications, Inc.
Long, S.  Confirmatory Factor Analysis, A Preface to LISREL #33.
Beverly Hills, CA:  Sage Publications, Inc.

Long, S.  Covariance Structure Models, An Introduction to LISREL #34.
Beverly Hills, CA:  Sage Publications, Inc.

Set 2

Tabacknick, B. G. & Fidell, L. S. (2001).  Using Multivariate
Statistics, Fourth Edition.  New York:  Harper Collins Publishers,
Inc. [T&F]

Additional Reference Books

Abelson, R. P. (1995).  Statistics as Principled Argument. Hillsdale,
NJ: Lawrence Erlbaum Associates, Inc.

Cooley, W. W. and Lohnes, P. R. (1985).  Multivariate Data Analysis
(2nd. ed.) New York, NY:  John Wiley and Sons, Inc.

Grimm, L. G. and Yarnold, P. R. (1995).  Reading and Understanding
Multivariate Statistics.  DC: American Psychological Association.

Hair, J. F., Anderson, R.E., Tatham, R.L. & Black, W.C. (1992).
Multivariate Data Analysis, (3rd. ed.), Macmillan Publishing Company,
New York, NY.

Harris, R.J. (1985).  A Primer of Multivariate Statistics, (2nd.
ed.), Orlando, FL., Academic Press.

Loehlin, J. C. (1992).  Latent Variable Models:  An Introduction to
Factor, Path and Structural Analysis. (2nd. ed.), Hillsdale, NJ:
Lawrence Erlbaum Associates, Inc.

Morrison, D. F. (1989).  Multivariate Statistical Methods, (2nd.
ed.), New York, NY:  McGraw-Hill Publishing Company

Pedhazur, E.J. (1982).  Multiple Regression in Behavioral Research:
Explanation and Prediction, Second Edition.  New York:  Holt,
Rinehart and Winston.

Pedhazur, E. J. and Schmelkin, L. (1991).  Measurement, Design, and
Analysis:  An Integrated Approach, Hillsdale, NJ: Lawrence Erlbaum
Associates, Inc.

Porter, T. M. (1995).  Trust in Numbers:  The Pursuit of Objectivity
in Science and Public Life.  Princeton, NJ:  Princeton University

Stevens, J. (1992).  Applied Multivariate Statistics for the Social
Sciences, (2nd. ed.), Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.

Tentative Course Outline and Schedule

Week 1		Introduction and Overview
• Students inventory of interests and experience with research,
statistics and measurement
• Taxonomy of Multivariate Techniques
• Review of univariate analysis techniques
• Assumptions underlying multivariate techniques
Readings:	[T&F: Chap. 1 & 2]

Week 2-3
1/20			Making Claims with Statistics and
• Function of Statistics – Meaning of Measurement
[Abelson:  Chap.1] – on reserve
[Porter:  Chap.4] – on reserve

Matrix Algebra

• Operations, Order, Trace, Determinant
• Sums of Square and Cross-Product (SSCP)
• Inverse, Rank, Eigen Values, Eigen Vectors
Readings:	[T&F: Appendix A]

Weeks 4-6
Multiple Regression

• Basic model, assumptions

• Analysis of the residuals

• Outliers, Multicollinearity
• Types of Multiple Regression
• Part and Partial Correlation
Readings:	[T&F: Chap. 4 & 5]


Weeks 7-8		
Hotelling's T2 and Manova


Readings:	[T&F: Chap. 9]

Week 9-10		
Discriminant Analysis


Readings:	[T&F: Chap. 11]


Weeks 11-12		
Principal Component and Exploratory Factor Analysis


Readings:	[T&F: Chap. 13]


Week 13-15		
Structural Equation Modeling

• Confirmatory Factor Analysis

• Covariance Structure Models

Readings:	[T&F: Chap. 14]

Week 16			

Course Assignments and Evaluation

I expect all assigned readings to be done as specified in class for
each session.  Readings are assigned to complement in-class
presentations and discussions, and to formalize understanding of the

As an enrolled student, you will complete two written assignments,
and two examinations.  The assignments are designed to evaluate your
conceptual understanding of the statistical analysis procedures, the
computations involved, how the analyses relate to the research
questions as well as the nature of the interpretations and inferences
made based on the analysis of data.  Short homework (e.g., matrix
algebra exercises, reading research articles) will also be assigned
for some of the topics and will have to be turned in on a timely

Each assignment will be evaluated according to a set of criteria that
will be communicated as part of the assignment.  The assignments,
homework, and examinations will contribute to the final grade as

	Regression assignment:	20%
	EFA assignment		20%
	Homework		10%
	Examination #1		25%
	Examination #		25%

Grading procedures are in accordance with the Bulletin for the
Graduate Program of the School of Education.  “Incomplete” will not
be granted except for extremely unusual circumstances.  Plagiarism
will result in an automatic “F” for the course.

Other Guidelines for the Course

Students are encouraged to discuss the course material among
themselves and to assist each other with data analysis.  The written
part of the assignments should, however, reflect individual student's

Labs are designed to provide additional assistance to students and
include: (1) assistance in setting up computer programs, (2)
assistance with homework and assignments, and (3) review of concepts
and procedures.  Students should come to lab prepared to ask