# EXPERIMENTAL DESIGN - 2019/0

Module code: MAT3021

## Module Overview

Fundamental topics in the design and analysis of experiments are introduced in this module. For a variety of statistical models, the structure of the model and applications are covered. Particular attention is given to practical issues. Statistical software is used to ensure that the emphasis is on methodological considerations rather than on calculation.

There are no pre-requisites for the module but students who have not taken MAT2002 General Linear Models will need to do some initial reading.

### Module provider

Mathematics

GODOLPHIN Janet (Maths)

### Module cap (Maximum number of students): 81

Independent Learning Hours: 117

Lecture Hours: 33

Semester 1

None

## Module content

Indicative content includes:

General Concepts:

• Principles of design and strategy of experimentation.

• Complete designs: m-way classification.

Designs Involving Blocking:

• Precision improvement by blocking

• Randomized block designs

• Incomplete block designs and balance

• Row column designs

• Latin square designs, Graeco-Latin squares (Euler's conjecture), Youden squares

Further Topics Involving Blocking:

• Efficiency

• Optimality criteria

• Connectivity

Factorial Designs:

• Principles and advantages of factorial designs

• Two level factorial systems

• Fractional factorial designs and aliasing

• Confounding factorial effects with block effects

A Selection Of One Or More Specialised Topics:

• Resolvable designs including Affine resolvable designs and Alpha designs

• Robust design and Taguchi methods

• Analysis of covariance

• Binary response data

• Crossover designs and carryover effects

## Assessment pattern

Assessment type Unit of assessment Weighting
Examination EXAMINATION 80
Coursework GROUP COURSEWORK 20

N/A

## Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

• Analytical ability by solution of unseen problems in the exam.

• Subject knowledge through the recall of key definitions, theorems and their proofs.

• An understanding of practical considerations when designing an experiment.

• The ability to analyse data, to interpret the analysis and report comprehensively on the results.

Thus, the summative assessment for this module consists of:

• One two hour examination (students have the choice of three questions out of four to contribute to exam mark) at the end of the semester; weighted at 80% of the module mark.

• One group coursework; weighted at 20% of the module mark.

Formative assessment and feedback

Students receive written feedback via a number of marked unassessed coursework assignments over an 11 week period. Formative guidance and feedback is given at specific stages of the group coursework.

## Module aims

• Provide students with a detailed understanding of the principles of experimental design.
• Give students practical experience of planning, conducting and analysing an experiment using a BIBD.
• Equip students with the tools and techniques to be able to design and analyse appropriate experiments in a range of situations.
• Cover the theory behind the analysis of data from various models.

## Learning outcomes

 Attributes Developed 1 Demonstrate an advanced understanding of principles of experimental design. KCT 2 Demonstrate knowledge of theory underlying analysis of experimental designs. K 3 Assess the properties of a given design. KCP 4 Critically assess the estimability capabilities of competing factorial and fractional factorial designs for use in a given situation. KCT 5 Plan and conduct a BIBD to investigate a simple problem. KCP 6 Analyse experimental data and interpret and explain the results in a way comprehensible to a layman. KCPT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

## Methods of Teaching / Learning

The learning and teaching strategy is designed to provide:

• A comprehensive treatment of principles and theory of experimental design.

• Experience in problem solving for the cognitive skills.

• Practical experience in experimental design and analysis.

The learning and teaching methods include:

• 3 x 1 hour contact sessions per week x 11 weeks. The majority of the sessions are lectures during which printed lecture notes are augmented. Remaining sessions are computer lab sessions where students gain experience in using R to analyse data from experimental designs.

• Group coursework to give students practical experience of experimental design.

• Several pieces of unassessed coursework to give students experience of using techniques introduced in the module and to receive formative feedback.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.