Design of Experiments
Kaltenbach Hans-Michael, Lecturer
Description
Abstract
The course introduces 'classical' statistical design of experiments, particularly designs for blocking, full and fractional factorial designs with confounding, and response surface methods. Topics covered include (restricted) randomization and blocking, sample size and power calculations, confounding, and basics of analysis-of-variance methods for analysis including random effects and nesting.
Objective
Students will learn about the statistical basics of designing and analyzing experiments with multiple qualitative and/or quantitative variables. Students will be able to construct designs for efficiently identifying important influence factors in their experiments, use sequential designs for optimizing experimental conditions, and correctly handle analyses with nested sampling or involving multiple comparisons.
Content
The course introduces the basics of statistical design of experiments. We will start by discussing the role of randomization for the validity of inferences, see how replication (i.e., sample size) affects the precision of estimates that can be made, how we deal with nested replication (for example, taking several measurements on the same animal), and how we correctly handle multiple comparisons based on the same data.
We will then discuss how restrictions of randomization lead to blocked designs, which serve to improve precision of comparisons between experimental conditions. Such designs are also important to avoid confounding of the experimental effect of interest with other effects of no interest, e.g., to handle batch effects that are common in biological experimentation.
Next, we learn how to design efficient experiments with multiple factors of interest. In contrast to a one-variable-at-a time approach, factorial designs allow investigation of multiple factors simultaneously, and under some assumptions on the interplay of the factors, we may even get away with only a fraction of all possible factor combinations while still getting all the information we need.
We then discuss optimizing the combination of factors with respect to some response function, such as optimizing the composition of a medium solution to achieve maximum growth rate. Response surface methods offer an efficient and systematic way of finding optimal conditions with low effort through sequential experimentation; they are also common in industrial (engineering) applications.
Throughout the course, we will touch on several additional topics without getting into much detail, such as designs that are `optimal¿ for either inference or prediction, and designs where experimental conditions are nested (e.g., split-plot designs).
The course assumes familiarity with the content of a typical introductory course in statistics: distributions and random variables, estimators and confidence intervals, hypothesis testing using p-values and false positives/negatives, and basics of linear regression or analysis of variance.
Lecture material
The lecture material is available here.
Literature
Main text
Additional texts
- D. R. Cox: Planning of Experiments, Wiley
- G. Casella: Statistical Design, Springer
- H. R. Lindman: Analysis of variance in complex experimental designs, Freeman (now Springer)
- Gary W. Oehlert: A first course in design and analysis of experiments, Freeman (http://users.stat.umn.edu/~gary/Book.html)
Timings
Lecture Q&A and Tutorials: Thursdays starting 14:15 (ZOOM)