This module runs in Term 2 and 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.
Pre-requisites:
Statistics Students: ST218 Mathematical Statistics A AND ST219 Mathematical Statistics B
Non-Statistics Students: ST220 Introduction to Mathematical Statistics
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.
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 exigencies 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 application areas will be given throughout, with an emphasis on analysis using R.
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
The module will typically cover:
By the end of the module, students should be able to:
View reading list on Talis Aspire
-Specify the model, construct the design matrix and estimate the parameters of any design based on a general linear model.
-Access design and analysis software that will take the computational labour out of both tasks.
-Communicate the advantages/disadvantages of particular designs to others; match designs with useful structures in most circumstances; interpret outputs from more complex (non-orthogonal) designs.
-Design and analyse simple experiments to test hypotheses, and interpret the outcomes; understand the power of factorial design structures, and the important concepts of confounding and aliasing.
| Type | Required | Optional |
|---|---|---|
| Lectures | 30 sessions of 1 hour (20%) | 2 sessions of 1 hour |
| Tutorials | 8 sessions of 1 hour (5%) | |
| Private study | 82 hours (55%) | |
| Assessment | 30 hours (20%) | |
| Total | 150 hours |
Weekly revision of lecture notes and materials, wider reading, practice exercises and preparing for examination.
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Students can register for this module without taking any assessment.
| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
| Assignment 1 | 10% | 15 hours | Yes (extension) |
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The assignment will contain a number of questions for which solutions and / or written responses will be required. |
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| Assignment 2 | 10% | 15 hours | Yes (extension) |
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The assignment will contain a number of questions for which solutions and / or written responses will be required. |
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| In-person Examination | 80% | No | |
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The examination paper will contain four questions, of which the best marks of THREE questions will be used to calculate your grade.
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| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
| In-person Examination - Resit | 100% | No | |
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The examination paper will contain four questions, of which the best marks of THREE questions will be used to calculate your grade.
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Marked assignments will be available for viewing at the support office within 20 working days of the submission deadline. Cohort level feedback and solutions will be provided, and students will be given the opportunity to receive feedback via face-to-face meetings.
Solutions and cohort level feedback will be provided for the examination.
If you take this module, you cannot also take:
This module is Optional for:
This module is Option list A for:
This module is Option list B for:
This module is Option list C for:
This module is Option list D for:
This module is Option list E for:
This module is Option list F for: