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School of Mathematics

# MATH30004 - 2006/2007

General Information
• Title: Analysis of Designed Experiments
• Unit code: MATH30004 (semester 2)
• Credits: 10
• Prerequisites: MT2131, 257, MATH30341 (ex-UMIST), MT2131, MT2232, MATH30341 (ex-VUM)
• Co-requisite units: None
• School responsible: Mathematics
• Member of staff responsible: Dr Peter Neal (Ferranti C.15, Tel: 63634)
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## Specification

### Aims

To introduce the student to the principles and methods of statistical analysis of designed experiments.

### Brief Description of the unit

Experiments are carried out by investigators in many fields including agriculture, industry, education, psychology and medicine. In such experiments the results are affected both by the choice of factors (either predetermined or random) and experimental error (such as measurement error or inherent randomness between experimental units). Statistical analysis of data collected from such designed experiments is important in understanding and interpreting the experimental results and also in the development of well designed experiments.

### Learning Outcomes

On successful completion of the course students will,

• given the description of how a set of data were collected, be able to:
• recognise what design was followed,
• comment on the shortfalls of the design used,
• decide what assumptions are appropriate in modelling the data,
• perform the appropriate analysis;

• be familiar with the principles of:
• randomisation and replication,
• nested designs,
• block designs,
• factorial designs and fractional layouts.

### Syllabus

1. Basic concepts; Definitions. [2]
Treatment, factors, plots, blocks, precision, efficiency, replication, randomisation and design.
2. Completely randomised design. [3]
Fixed and random effects, contrasts, ANOVA table.
3. Factorial designs. [4]
General factorial experiment; fixed and random effects; interactions.
4. Nested designs. [3]
5. Blocking. [7]
• Orthogonal designs: Randomised complete block designs; Latin square designs; extensions of the Latin square design.
• Non-orthogonal designs: Balanced incomplete block designs.
6. 2m factorial experiments. [5]
Confounding; fractional replication; aliasing.

### Textbooks

W. G. Cochran and G. M. Cox, Experimental Designs, Wiley,
C. R. Hicks, Fundamental Concepts in the Design of Experiments, OUP (fourth edition),
D. C. Montgomery, Design and Analysis in the Design of Experiments, Wiley (fourth edition).

### Teaching and learning methods

Two lectures per week plus one weekly examples class.

Assessment
Coursework: weighting within unit 20%
Two hour end of semester examination: weighting within unit 80%

## Arrangements

Online course materials are available for this unit.