Midlands State University
Faculty of Science & Technology
Mathematics Department
Course Code: HMT417
Course Title: MULTIVARIATE ANALYSIS
Course Outline
Multivariate data, descriptive statistics, graphical techniques. Random vectors and matrices, their
expectations and properties, expected values of the sample mean and sample covariance matrix. Multivariate
normal distribution and its properties, sampling distribution of sample mean and sample covariance matrix.
Wishart distribution. Transformation to near normality, testing for normality. Inferences about mean vector:
Hotelling’s T2 distributions and likelihood ratio test , comparison with one dimensional case, confidence
regions and simultaneous comparisons of component means: Bonferroni method of multiple comparison.
Comparison of several multivariate means: comparing mean vectors from two population means (one-way
MANOVA). Simultaneous confidence intervals for treatment effects, profile analysis, ideas of two-way
MANOVA. Review of eigenvalues and vectors, spectral decomposition of symmetric matrix. Principal
component analysis. Introductory study and use of one technique from; Factor analysis, Canonical
correlation analysis, Discriminant analysis.
Lecture Times: as per Time Table, attendance is compulsory
( Monday 10-12 am Wednesday 10-12 am) Maths Buliding
Assessment: Coursework (25%)- from assignments, projects & tests, and End of Semester examination
(75%)
References
 Graybill, F. A. (1977) Introduction to matrices with applications in Statistics, Wadsworth, Belmont,
California
 Johnson, R. A. & Wichern, D. W. (1988): Applied Multivariate Statistical Analysis, Prentice Hall
Inc, Eaglewood Cliff, New Jersey
 Morrison, D. F. (1990) Multivariate Statistical Methods, MacGraw Hill International Additions,
Singapore
 Muiread, R. J. (1982) Aspects of Multivariate Statistical Theory, John Wiley and Son, New York
 Chimedza, C. (2001) Multivariate Analysis, ZOU Module, Harare Zimbabwe
 Bock, R. D. (1975). Multivariate statistical methods in behavioral research, N.Y.: McGraw Hill.
 Carroll, J. D., Green, P. E. & Chaturvedi, A. (1997). Mathematical tools for applied multivariate
analysis. (2nd ed.) N.Y.: Academic Press
 Dillon, W. R., & Goldstein, M. (1984). Multivariate analysis: Methods and applications. N. Y.:
Wiley.
 Flury, B. (1997). A first course in multivariate statistics. N.Y.: Springer
 Gifi, A. (1990). Nonlinear Multivariate analysis. Chichester: Wiley
 Gnanadesikan, R. (1997). Methods for statistical data analysis of multivariate observations, (2nd ed.)
N.Y.: Wiley.
 Hair, Anderson, Tatham, Black (1998). Multivariate Data Analysis, (5th ed.) Prentice Hall