Study level
BAC +5
ECTS
2 credits
Component
Faculty of Science
Description
A design of experiments is the ordered sequence of trials in an experiment, the aim of which is to test the validity of a hypothesis by reproducing a phenomenon and varying one or more parameters. Each trial produces data, and all the data produced during an experiment must be analyzed using rigorous methods to validate or invalidate the hypothesis. This experimental approach makes it possible to acquire new knowledge by confirming a model with a good economy of means (the lowest possible number of trials, for example).
Starting with a simple problem, the module develops the methodological and statistical tools needed to support increasingly complex hypotheses as optimally as possible. These methodologies are implemented using the R statistical language.
Hourly volumes* :
CM: 15h
Practical: 5h
Objectives
Give students the skills they need to understand the main concepts of experimental design and how to use the tools of inferential statistics to design and analyze experimental designs.
At the end of this module, students should be able to choose an experimental design adapted to their problem and analyze the results in a complete, rigorous and intellectually mastered way.
Necessary prerequisites
HAC712X: Chemometrics, statistical data analysis, experimental design
Knowledge control
CC-I
Syllabus
Introduction to experimental design: Hotelling's weighing problem. Review of the concepts of response surface, experimental error, modeling, confidence interval and hypothesis testing.
Complete experimental designs: presentation. 2p factorial designs, p = 1, 2, ... Multi-level factorial designs: K1* K2 *...* Kp. Notions of interaction and synergy. Statistical analysis: analysis of variance, validation of assumptions.
Fractional experimental designs: presentations, motivations, limitations. Factorial designs 2p-k factorial designs, complete and incomplete block designs, Latin squares, Greco-Latin squares, Youde squares. Statistical analysis: analysis of variance, validation of presuppositions.
Response surface: first- and second-degree models. Estimation and inference. Star designs, D-optimality and D-optimal designs. Mixture designs.
Further information
Administrative contact(s) :
Secretariat Master Chemistry
https://master-chimie.edu.umontpellier.fr/