MA310-6-AU: EXPERIMENTAL DESIGN
Department: Mathematical Sciences
Essex credit: 15
ECTS credit: 7.5
Available to Study Abroad / Exchange Students: Yes Pre-requisites: MA207
This course is concerned with the application of linear models to the
analysis of experimental data. This analysis seeks to identify the
underlying courses in the variation of the values of a response
variable, y, by identifying variations in various background variables.
The models assume normally distributed measurement errors and therefore
involve the normal, chi-squared, t and F distributions.
The analysis is greatly simplified if the explanatory variables are
orthogonal to one another. This can be achieved if the measurements made
are at carefully chosen combinations of the background variables. This
is the experimental design of the course's title. All the commonly used
designs will be studied in the course.
On completion of the course students should be able to:
-Identify a simple experimental design
-Construct an appropriate ANOVA table
-Perform multiple comparisons tests
-Utilize orthogonal polynomials
-Distinguish between fixed effects and random effects
-Construct full and partial factorial designs in the presence of blocks
Interrelations between Normal, chi-squared, t and F distributions.
Understanding the ANOVA table.
Contrasts, orthogonality, and subdivision of the treatment sum of squares.
Orthogonal polynomials and curvilinear regression.
Multiple comparison tests.
Random effects models.
Randomized block designs.
Two factors with interactions.
Repeated measures. Latin squares, Graeco-Latin squares.
Balanced incomplete block designs.
Philosophy. Notation. Underlying model.
Analysis with and without replication. Confidence and prediction intervals.
Factorials and blocks. Replicates of confounded designs.
Partial confounding. Constructing a balanced design.
Fractional replicates. Aliases. Fractions in blocks.
Optimisation with quantitative factors. Augmented designs. Steepest ascent.
Learning & Teaching Methods
This course consists of 20 lectures, 5 example sessions, and 5 Problem classes. In the Summer term 3 revision lectures are given.
20 per cent Coursework Mark, 80 per cent Exam Mark
20 percent Coursework mark consisting of 5 fortnightly sets of coursework where the best 3 out of 5 count (6.67% each).
Information about coursework deadlines can be found in the "Coursework Information" section of the Current Students, Useful Information Maths web pages: Coursework and Test Information
Exam Duration and Period
2:00 hour exam during Summer Examination period.
Available independently to Socrates/IP students spending all relevant terms at Essex.
- Recommended reading:
Montgomery, D.C. (2005) Design and Analysis of Experiments, 6th Edn. J. Wiley.
Cox, D.R. (1958) Planning of Experiments, J. Wiley.
Fisher, R.A. (1966) The Design of Experiments, 6th Edn. Hafner.
Fox, J., (1997) Applied Regression Analysis, Linear Models, and Related Methods, Sage.