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School of Mathematics

# MATH38082 - 2010/2011

General Information
• Title: Design and Analysis of Experiments
• Unit code: MATH38082
• Credits: 10
• This course unit cannot be taken as well as MATH48082 which is a level 4 version of the same course unit.
• Prerequisites: MATH20701, MATH20802. Knowledge of MATH38011 Linear Statistical Models is helpful but not essential.
• Co-requisite units: None
• School responsible: Mathematics
• Members of staff responsible: Dr. Alex Donev
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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 researchers in many fields including biology, medicine, chemistry, physics, engineering and agriculture. In such experiments the results are affected both by the choice of factors to study and experimental error (such as measurement error or inherent randomness between experimental units). Choosing a good experimental design ensures that the aim of the study where it is used is achieved. Moreover, the statistical analysis of data collected from such designed experiments is simple, easier to interpret and the experimental resources are spent most efficiently. The main principles for designing and analyzing experiments will be introduced. Various standard experimental designs and the analysis of data obtained using them are covered.

### Learning Outcomes

On successful completion of this course unit 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,
• response surface designs.

None.

### Syllabus

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

### Textbooks

• A. C. Atkinson, A. N. Donev, R. D. Tobias (2007). Optimum Experimental Designs, With SAS. OUP.
• G. Cassela (2008). Statistical Design. Springer.
• G.M. Clarke and R. E. Kempson (1997). Introduction to the Design and Analysis of Experiments. Arnold.
• D. C. Montgomery (1997). Design and Analysis in the Design of Experiments, (4th edition).

### Teaching and learning methods

Two lectures and one examples class each week. In addition students should expect to spend at least four hours each week on private study for this course unit.

### Assessment

Coursework: weighting 10%
End of semester examination: two hours weighting 90%

## Arrangements

On-line course materials for this course unit.