MATH48082 - 2007/2008

 

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 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.

Future topics requiring this course unit

None.

Syllabus

1. Basic concepts; Definitions. [2 lectures]
   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. [6]
   General factorial experiment; fixed, random and mixed effects; interactions.
4. Nested designs. [5]
   Nested and crossed factors.
5. Blocking. [10]
   Orthogonal designs: Randomised complete block designs; Latin square designs; extensions of Latin square designs; factorial structure.
   Non-orthogonal designs: Balanced incomplete block designs; Youden square design.
6. 2^m factorial experiments. [4]
   Confounding; fractional replication; aliasing.
7. Response surface designs. [3]

Textbooks

• W. G. Cochran and G. M. Cox, Experimental Designs, Wiley 1957.
• C. R. Hicks, Fundamental Concepts in the Design of Experiments, (4th edition), OUP 1973.
• D. C. Montgomery, Design and Analysis in the Design of Experiments, (4th edition), Wiley 1997.

Teaching and learning methods

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

Assessment

Coursework: weighting 20%

End of semester examination: two and a half hours weighting 80%

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