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# Course information

### Course information / Aim

In real life applications, it is very common that test results are influenced by both controllable and non-controllable factors. This course intends to provide knowledge of how good experimental design combined with appropriate random models for the test results can study the influence of controllable factors and to a certain extent compensate for the impact of non-controllable factors. Through careful planning, the amount of measurement data can often be reduced, which can be of great importance in practice. Evaluation of a model's validity is also an important part of the course. Many analysis methods are based on assumptions about normal distribution, which is sometimes not reasonable. The course also provides knowledge of so-called non-parametric methods that do not require exact knowledge of the distribution of the random variables behind the observed values. Power derivations in connection with the planning of studies are also included in the course.

The course is intended to give an introduction to the design and analysis of factorial experiments. The emphasis is on design of experiments, selection of model, analysis of observed data, ability to interpret the results and to draw conclusions. Knowledge of alternative nonparametric methods is also essential. By the end of the course, the student should be able to:
• design factorial experiments of different types using appropriate randomization;
• choose a suitable model to describe observed data taking into account the design of the experiment that generated the data, then perform an appropriate analysis and draw conclusions by means of hypothesis testing and construction of confidence intervals;
• make multiple comparisons of parameters with a given simultaneous confidence level;
• check model adequacy and need of transformation of data;
• design, conduct and analyse complete and reduced 2^k factorial experiments;
• use nonparametric methods to analyse data of different types and discuss the applicability of the methods;
• use generalized linear models to analyse data, interpret the analyses and discuss the adequacy of the methods;
• use power calculations to determine the sample size for certain kinds of random experiments;
• use statistical software (e.g., Minitab or Matlab) to analyse data from factorial experiments for both parametric and nonparametric methods.

### Organisation

The teaching consists of lectures (22h), example classes (22h) and mandatory computer exercises (12h).

During the lectures theory and methods are presented together with applications (examples). In the example classes concrete examples, intended to illustrate the theory are given and should be solved by the participants. The computer exercises are mandatory computer example classes which will give practical experience with implementing and using the methods in Minitab (or Matlab).

### Examination

To pass the course you have to pass the computer exercises (LAB1 1hp), the hand in assignments (UPG1 1hp) and a written exam (TEN1 4hp). The written exam consists of four to six problems which are based on the material discussed in the course.

Sidansvarig: martin.singull@liu.se