# ST410: Designed Experiments with Advanced Topics

###### Lecturer(s): Dr Rachel Hilliam

Availability: Only available to students who have NOT taken ST305

Prerequisite(s): ST218/219 Mathematical Statistics A&B

Commitment: 30 one-hour lectures, plus weeky one-hour seminars / practicals. This module runs in Term 2.

Background: Designed experiments are used in industry, agriculture, medicine and many other areas of activity to test hypotheses, to learn about processes and to predict future responses. The primary purpose of experimentation is to determine the relationship between a response variable and the settings of a number of experimental variables (or factors) that are presumed to affect it. Experimental design is the discipline of determining the number and order (spatial or temporal) of experimental runs, and the setting of the experimental variables.

Content: This is a first course in designed experiments. The elementary theory of experimental design relies on linear models, while the practice involves important eliciting and communication skills. In this course we shall see how the theory links common designs such as the randomised complete block and split-plot to the underlying model. The course will commence with a review of linear model theory and some simple designs; we shall then examine the basic principles of experimental design and analysis, e.g. the concepts of randomisation and replication together with the blocking in designs and the combination of experimental treatments (factorial structure). Classical design structures are developed through the separate consideration of block and treatment structure, and the use of analysis of variance to explore differences between treatments for different types of design is explored. Throughout, diagnostic and analysis methods for the examination of practical experiments will be developed. A significant part of the course will be spent developing aspects of factorial design theory, including the theory and practice of confounding and of fractional designs. We will see how the exigiencies of design in an industrial context have led to further theory and different emphases from classical design. This will include the use of regression in response surface modelling. Further topics such as repeated measures, non-linear design and optimal design theory may be included if time allows. Practical examples from many different applications areas will be given throughout, with an emphasis on analysis using R.

Aims: This course aims to give students a sound understanding of experimental design, both theoretical and practical. The course will explore the method of analysis of variance and show how it is structurally linked to particular types of design. The combinatoric properties of designs will be explored, and the impact of computers on classical design considered. Some exploration of the matrix theory of design will also be undertaken.

Objectives: By the end of the course students will be able to:

• Describe the basic principles behind designed experiments
• Show the relationship between a designed experiment, the underlying linear model and the analysis of the resulting data
• Construct the design matrix for a simple experiment and estimate the model parameters
• Perform an analysis of variance on standard experimental designs
• Distinguish between different types of design and recognise their efficiency / utility
• Perform diagnostic tests on the results from a designed experiment.

Books:

• G Clarke & R Kempson, Introduction to the Design and Analysis of Experiments, Arnold, 1996.
• DC Montgomery, Design and Analysis of Experiments, Wiley, 2005, 2009, 2012

Students will be given selected advanced material for further study and examination.

Assessment: Two assignments worth 10% each and 80% by 2-hour examination.

Deadlines: Assignment 1: Week 7 of Term 2. Assignment 2: Week 1 of Term 3. Other exercises will be provided and discussed during the seminars.

Feedback: Feedback on both assignment 1 and 2 will be returned after 2 weeks, following submission.

You may also wish to see:
resources for current ST410 students (restricted access)