Experimental Design (B-KUL-G0B68A)
This course gives a comparative overview of the most used experimental designs and their analysis, with an emphasis on the design issues. It learns students which designs are most appropriate for a particular experimental situation, and how the resulting data should be analysed (using statistical software).
Students have good knowledge about linear algebra (simple matrix operations, inverses), the basic principles of probability and statistics, and about the basics of regression and analysis of variance (or about linear models in general). They should be familiar with the concepts of confidence intervals, hypothesis testing, p-values, the fitting of simple linear models and the interpretation of fitting diagnostics. Familiarity with at least one statistical package is an advantage.
Beginning conditions: Students should have had an introductory statistics course and a course covering the basics of regression and analysis of variance. The course Linear Models: Regression Analysis and Analysis of Variance is sufficient as a prerequisite (although other course(s) may also be sufficient).
Slides, transparencies, courseware
Examples and samples
Toledo / e-platform
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Designing an experiment: reasons and procedures
- designed experiments versus observational studies
- role of randomization
- steps in designing an experiment
- criteria for comparing designs, types of optimality
Completely randomized designs
- randomization: practical issues
- power and sample size
- analysis: contrasts, multiple comparisons, diagnostics
- factorial structure, the concept of interaction
- analysis of balanced factorials
- designs with single replicates
- pooling terms into error
- analysis issues with unbalanced data
Mixed effects models
- random effects
- estimation of variance components
- appropriate tests
Designs with nested factors
- the concept of nesting
- analysis of nested designs
Nesting, mixed effects and the appropriate tests
- Hasse diagrams and expected mean squares
Complete block designs
- Latin Square designs
- other row/column designs
Incomplete block designs
- balanced incomplete block designs
- other incomplete block designs
Split plot designs
- what is a split plot
- analysis of split plot designs
- generalizations of split plot designs: repeated measures and crossover designs
- 2k-p fractional designs
- confounding, resolution, foldover
- Plackett-Burman designs
Response surface designs
- designs for second order models
- designs for mixtures
Description of learning activities
The students are expected to master the concepts and understand the properties of and the differences between the different designs by studying the material from the lectures.
Through the homeworks they are expected to learn how to theory learned should be applied to obtain actual designs (this includes setting up and using a randomization procedure). In other homeworks they are given a description of an experiment and the data obtained, and they should set up an appropriate model, perform an appropriate analysis with the help of a statistical software package and summarize these in a report. The students will also use a specially developed software tool to perform virtual experiments, which allows them to make and compare experimental setups and obtain realistic data in a very convenient way.