Introductory description

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

Module web page

Module aims

Outline syllabus

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:

• A review of linear model theory and some simple design,
• Basic principles of experimental design and analysis such as randomisation and replication,
• Blocking in designs and combination of experimental treatments,
• Factorial design theory including theory and practice of confounding and fractional designs,
• Analysis of Variance to explore differences between treatments for different types of designs,
• Regression in response surface modelling.
  . Specific higher-level material for ST410 (not for ST305 which is the third year variant) include principles of robust design and Analysis of Covariance.
  If time allows additional topics may be included such as repeated measures, non-linear design and optimal design theory.

Learning outcomes

By the end of the module, students should 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.

Indicative reading list

View reading list on Talis Aspire

Subject specific skills

-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.

Transferable skills

-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.