Purpose
Experiments are conducted to discover how certain variables that can be controlled by the experimenter affect the values of one or more 'response' variables.
It is important that the objectives are clearly defined in terms of response and controlled variables before going further in the design of an experiment.
Experimental units
Experiments usually involve discrete 'experimental units'. Depending on the type of experiment, the experimental units could be:
There may be some known structure to the experimental units — for example, the people may have different ages or the plots of land may be in different parts of a farm with different soils or drainage.
The experimental units that will be used in an experiment are first selected. One or more response measurements will be made from each unit during the course of the experiment.
Controlled variables
In an experiment, the researcher is able to control the values of one or more variables that can potentially influence what happens to the unit during the course of the experiment. Simple experiments only have a single controlled variable but many experiments involve several variables that are controlled.
The controlled variables in an experiment are determined by its objectives and are called factors. They may be:
For each individual factor, its distinct values are called its levels.
In some experiments, the 'control' of an explanatory variable may arise only through the choice of experimental units. For example, in an experiment with animals, it may be decided to use 10 males and 10 females, in which case gender would be treated as a categorical explanatory variable.
Design
The combination of levels for all factors that are used with any experimental unit are collectively called a treatment and we say that the experimenter can control which treatment to apply to each experimental unit.
In a simple experiment with a single controlled factor, the treatments are simply the factor levels. However in an experiment that controls the amounts of three trace elements (P, Na and Mg) applied to tomato plants, each possible combination of levels of the three elements is a separate treatment.
The experimental design is the method used to decide which treatment to apply to each experimental unit.
Response variable
One or more response measurements are made from each experimental unit, the measurements being dictated by the objectives of the experiment. The experiment aims to discover whether each factor affects the responses and, if so, by how much.
Although advanced methods exist to simultaneously analyse several response measurements, it is usually sufficient to examine the effects of the factors on each response separately.