Multivariate Design & Analysis PSY 614
T. Mark Beasley, Ph.D. Marillac Hall SB 36-E
E-Mail: beasleyt@stjohns.edu Voice:(718) 990-1478
Website: http://facpub.stjohns.edu/~beasleyt/index.html Fax: (718) 990-5926
Texts
(TF) Tabachnick, B, & Fidell, L. (2000). Using multivariate statistics (4th ed.). New York:
Allyn & Bacon.
(GSA) Green, S. B., Salkind, N. J., & Akey, T. M. (2000). Using SPSS for Windows: Analyzing
and understanding data (2nd ed.). Upper Saddle River, NJ: Prentice-Hall.
Supplementary Reading
(H) Huck, S. W. (2000). Reading Statistics and Research (3rd ed.). New York: Longman.
(MV) Mertler, C., & Vannatta, R. (2001). Advanced and multivariate statistical methods. Los
Angeles: Pyrczak Publishing. [Chapters will be available in the Reserve Room]
Other Valuable Sources:
(AF) Agresti, A., & Finlay, B. (1997). Statistical Methods for the Social Sciences (3rd ed.).
Upper Saddle River, NJ: Prentice-Hall.
COURSE OUTLINE for MULTIVARIATE STATISTICS (PSY 614)
I. Introduction to Multivariate Techniques: An Overview
A. Multivariate Research Questions vs. Multiple Univariate Research Questions
(TF1 MV1; AF10; Fish, 1988[10]; Huberty, 1994[15]; Huberty & Morris, 1989[16])
B. Overview of Techniques (TF2; MV2)
C. Canonical Correlation as the most general analytic technique
(Henson, 2000[11]; Knapp, 1978[19]; Thompson, 1991[29]).
II. Matrix Algebra (Matrix Algebra handout in Reserve Room; TF Appendix A).
A. Notation and Terminology
1. Types of Matrices; Order (dimensions) of a Matrix
a. Vectors
b. Square and Symmetric Matrices
c. Identity Matrix the matrix equivalent of 1.
d. Null Matrix the matrix equivalent of 0.
2. Matrix addition and subtraction, Matrix conformability.
Exact order must be matched.
3. Trace and Transpose of a Matrix.
4. Matrix Multiplication, Matrix conformability
a. Column of prefactor must match row of postfactor
b. Row of prefactor and column of postfactor
define the order of the product matrix.
c. A(NxK)B(KxJ) = AB(NxJ)
d. A′(KxN)A(NxK) = A′A(KxK) = Sum of Squares and Cross Products Matrix.
5. Inverse of a Matrix; Matrix “Division”
a. A(NxN)A-1(NxN) = A-1(NxN)A(NxN) = I(NxN), if N=1 then AA-1(NxN) = A/A = 1.
b. Not all square matrices have an inverse, they are singular.
c. Singularity one or more column(s) is a linear combination
of the other columns. This applies to rows as well.
c. Most symmetric matrices used in statistics do have an inverse.
d. Generalized inverse.
6. Eigenvalues and Determinants.
B. Univariate Procedures in Matrix Notation
