The University of Southampton
Social Sciences: Social Statistics & DemographyPart of Social SciencesPostgraduate study

# STAT6084 Multivariate Analysis

## Module Overview

This module aims to introduce you to the analysis and interpretation of multivariate data: measurements of p variables on each of n subjects. The module focuses on traditional normal-theory material which underpins many multivariate statistical methods. In addition, the use of three classical multivariate techniques - principal component analysis, discriminant analysis and cluster analysis - is considered in some detail. The module also involves some practical data analysis using the statistical software STATA.

### Aims and Objectives

#### Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• Techniques for displaying and summarising multivariate data
• Basic properties of multivariate distributions and in particular those of the multivariate normal and related distributions
• Standard multivariate hypothesis tests
• The classical methods of principal components analysis, discriminant analysis, and cluster analysis

#### Transferable and Generic

Having successfully completed this module, you will be able to:

• The ability to carry out and interpret the results from a principal component analysis, a discriminant analysis, and a cluster analysis
• The ability to analyse and solve problems
• The use of the statistical software STATA

### Syllabus

The module covers traditional normal-theory material and the application of several commonly used multivariate techniques. Topics covered are: simple plotting and display ideas for multivariate data, general (theoretical) properties of multivariate distributions, principal component analysis, the multivariate normal distribution and related distributions (Wishart and Hotelling’s distributions), maximum likelihood estimation, multivariate hypothesis testing, discriminant analysis, measures of multivariate distance, similarity, and clustering methods.

### Learning and Teaching

#### Teaching and learning methods

This module is delivered through a combination of lectures, tutorials, and computer workshops. The lectures cover the theoretical aspects of the course; practice exercises that complement the lecture material are discussed during the tutorials. The computer workshops involve analysis of data and application of the techniques introduced in the lectures using STATA.

You will require access to the STATA software, which is available on the University's computer workstations. Note that this software is not currently available for download to your own computer for use with your studies.

There is no single set text book for the module, although one useful text book which covers much of the syllabus is R. A. Johnson and D. W. Wichern (2007). Applied Multivariate Statistical Analysis (6th edition), Pearson Education.

1. C. Chatfield and A. J. Collins (1980). Introduction to Multivariate Analysis, London: Chapman and Hall/CRC.
2. L. C. Hamilton (2013). Statistics with Stata (Version 12), Cengage.
3. R. A. Johnson and D. W. Wichern (2007). Applied Multivariate Statistical Analysis (6th edition), Pearson Education.
4. W. J. Krzanowski (2000). Principles of Multivariate Analysis: a User’s Perspective (revised edition), Oxford: Clarendon.
5. B. F. J. Manly (2004). Multivariate Statistical Methods: a Primer (3rd edition), Chapman and Hall/CRC.
6. K. V. Mardia, J. T. Kent and J. M. Bibby (1979). Multivariate Analysis (3rd edition).  London: Academic Press.

### Assessment

#### Assessment methods

Assessment Method Hours % contribution to final mark Feedback
Exam 2 hours hour(s) 100%

Referral Method: By examination

Method of Repeat Year: Repeat year internally. Repeat year externally.

### Costs

#### Costs associated with this course

Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.

Please also ensure you read the section on additional costs in the University’s Fees, Charges and Expenses Regulations in the University Calendar available at www.calendar.soton.ac.uk.