The University of Southampton
Courses

# STAT6084 Multivariate Analysis

## Module Overview

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

#### Module Aims

To introduce you to the analysis and interpretation of multivariate data: measurements of p variables on each of n subjects

#### Learning Outcomes

##### Learning Outcomes

Having successfully completed this module you will be able to:

• Demonstrate knowledge and understanding of the techniques for displaying and summarising multivariate data
• Demonstrate knowledge and understanding of the basic properties of multivariate distributions and in particular those of the multivariate normal and related distributions
• Demonstrate knowledge and understanding of standard multivariate hypothesis tests
• Demonstrate knowledge and understanding of the classical methods of principal components analysis, discriminant analysis, and cluster analysis
• Carry out and interpret the results from a principal component analysis, a discriminant analysis, and a cluster analysis
• Analyse and solve problems
• Use 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, random vectors and matrices, random sampling from a multivariate population, 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.

None.

### 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.

TypeHours
Teaching22
Independent Study78
Total study time100

Software requirements. 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.

C. Chatfield and A. J. Collins (1980). Introduction to Multivariate Analysis.

W. J. Krzanowski (2000). Principles of Multivariate Analysis: a User’s Perspective.

B. F. J. Manly (2004). Multivariate Statistical Methods: a Primer.

L. C. Hamilton (2013). Statistics with Stata (Version 12).

R. A. Johnson and D. W. Wichern (2007). Applied Multivariate Statistical Analysis.

K. V. Mardia, J. T. Kent and J. M. Bibby (1979). Multivariate Analysis.

### Assessment

#### Summative

MethodPercentage contribution
Exam  (2 hours) 100%

#### Repeat

MethodPercentage contribution
Exam  (2 hours) 100%

#### Referral

MethodPercentage contribution
Exam  (2 hours) 100%

#### Repeat Information

Repeat type: Internal & External

### Costs

#### Costs associated with this module

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.

In addition to this, students registered for this module typically also have to pay for:

##### Approved Calculators

The University approved calculator is required for the exam.

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.

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