Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more.

## Experimental Design

When analyzing data we can distinguish two basic types of experiments: (1) observational experiments force the experimenter just to watch and listen, with no possibility to influence or select the observed variables. (2) In contrast to this, we may performe designed experiments, which allow a control of the level of variables applied to the experimental setup. Although in many practical situations the experimenter does not have any opportunity to control the variables, it is quite instructive to have a working knowledge on experimental designs and the analysis of the data obtained.

Here is a collection of the most important terms concerning experimental designs:

 response variable (dependent) variable of interest; is determined by the outcome of the experiment independent variables variables of the experiment which determine the behavior of the experimental setup; in experimental design literature independent variables are called factors factors variables of the experiment which determine the behavior of the experiment. Factors can be qualitative or quantitative factor levels factor levels are the values of a factor as used in a concrete experiment treatments if more than one factor is utilized, each treatment is a particular combination of factor levels of all involved factors. experimental unit an experimental unit is the object on which the response is observed.

A designed experiment is one for which the experimenter controls the treatments and the assignment of experimental units to the particular treatments.

The most important question in experimental design is how to set up the factor levels and how to assign the experimental units to the individual treatments. Several possibilities are commonly used:

• completely randomized design
• randomized block design
• factorial experiments

One major tool for statistical analysis of experimental designs is the analysis of variance (ANOVA).

Last Update: 2012-10-08