The University of Southampton
Courses

# MATH3014 Design and Analysis of Experiments

## Module Overview

A well-designed experiment is an efficient way of learning about the world. Typically, an experiment may involve varying several factors and observing the value of a response at settings of combinations of values of these factors. The mathematical challenge is then to choose which settings to use in order to gain the maximum information from the resulting data. Experiments are performed in all branches of science, engineering and industry. In recent years, traditional application areas such as agriculture, manufacturing, medicine and pharmaceutical science have been joined by bioinformatics, genetics, drug discovery, finance and economics. Problems of increasing size and complexity from these new areas have led to the development of many new methods for designing and analysing experiments. The aim of this module is to provide a grounding in the statistical and mathematical methods that underpin the design and analysis of experiments, before exploring a number of areas where recent and ongoing developments are taking place. These will include designs with large numbers of factors, designs with random blocking factors and designs generated through computer optimization. Mathematical criteria for quantifying the information available from a given design will be defined and explored, and will underpin much of the material in the module. Examples from a range of application areas will be used to motivate and illustrate the methods. The computer package SAS will be used for the practical design and analysis of experiments. SAS is a standard in many areas, including in the pharmaceutical industry, and for "business analytics" and data mining in finance and other sectors. Although MATH2010 is listed as a pre-requisite, interested students who have not taken that module are encouraged to discuss the module with the module Current Module Co-ordinator.

### Aims and Objectives

#### Module Aims

To provide a grounding in the statistical and mathematical methods that underpin the design and analysis of experiments, before exploring a number of areas where recent and ongoing developments are taking place.

#### Learning Outcomes

##### Learning Outcomes

Having successfully completed this module you will be able to:

• Encounter the principles of randomisation, replication and stratification, and understand how they apply to practical examples.
• Explore the general theory of factorial and block designs and understand this theory sufficiently to find appropriate designs for specific applications
• Evaluate designs using common optimality criteria and used them to critically compare competing designs
• Applied theory and methods to a variety of applications.
• Used the SAS statistical software to analyse common forms of experiments.

### Syllabus

Introduction, motivation and principles of designed experiments • Revision of regression and the linear model • Comparative experiments with a single factor - completely randomised designs - block designs (particularly balanced incomplete block designs) • Factorial experiments - including fractional factorial designs and block designs (at 2 levels) • Computer-generated designs and optimality criteria • Screening designs* - including orthogonal arrays and supersaturated designs • Response-surface methods • Introduction to optimal design and approximate theory *denotes topics where the material will be primarily covered in computer worksheets or workshops Applications and case studies will be used to motivate and illustrate throughout

### Learning and Teaching

#### Teaching and learning methods

Lectures, computer workshops and private study

TypeHours
Independent Study102
Lecture36
Tutorial10
Practical classes and workshops2
Total study time150

Atkinson, A., Donev, A. and Tobias, R. (2007). Optimum Experimental Designs, with SAS.

Kutner, M.H., Nachtsheim, C.J., Neter, J. and Li, W. (2004). Applied Linear Statistical Models.

Wu, C.F.J. and Hamada, M. (2000). Experiments - Planning, Analysis and Parameter Design Optimization.

Box, G. E. P., Hunter, J.S. and Hunter, W.G. (2005). Statistics for Experiments.

### Assessment

#### Summative

MethodPercentage contribution
Exam  (2 hours) 80%
Practice 20%

#### Referral

MethodPercentage contribution
Exam 100%

#### Repeat Information

Repeat type: Internal & External

#### Pre-requisites

To study this module, you will need to have studied the following module(s):

CodeModule
MATH2011Statistical Distribution Theory
MATH2010Statistical Methods I

### 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:

##### Books and Stationery equipment

Course texts are provided by the library and there are no additional compulsory costs associated with the module

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.