Structure of a simple experiment

The simplest type of experiment is conducted to assess the effect of a single factor on the response. A collection of experimental units is used and different levels of the factor are allocated at random to the experimental units. In many experiments, the same number of experimental units are used for each level of the factor but this is not essential.

This type of experimental is called a completely randomised experiment.

The repeat measurements at each factor level are called replicates.

When are completely randomised experiments used?

Completely randomised experiments are mostly used when the experimental units are either very similar or differ in ways that cannot easily be measured before the experiment is conducted. As a result, laboratory and engineering experiments often use a completely randomised designs.

If the experimental units are more variable and we have some information about their structure (e.g. if we can group them into blocks of similar units), there are better experimental designs that will be described in later chapters.

Even though completely randomised experiments are rarely used in disciplines such as agriculture in which there is structure to the available experimental units,

The method of analysis provides a good basis to methods that will be used for more complex experiments in later chapters.


Randomisation

A key aspect of a completely randomised experiment is the random allocation of treatments to experimental units. The diagram below illustrates this randomisation for an experiment with 6 replicates for each of the 5 factor levels.

Click Randomise experiment to randomly allocate the treatments to experimental units.

Notice that the six replicates of Level 1 are equally likely to be used in any six of the experimental units. If the treatments are allocated to the experimental units in any other way, the design is not a completely randomised one. For example, if treatments are allocated to ensure that all three units in a row get the same treatment, the design is not completely randomised and analysis of the resulting data will not be covered until a later chapter.

Examples

A few examples of completely randomised experiments are shown below.

Problem Experiment Randomisation
An apple grower wants to assess how different types of pesticide affect the yield of apples. Each of 4 types pesticides is used on 10 different apple trees. The number of apples produced by each of the 40 trees is recorded. The 10 trees given each pesticide were randomly chosen from the 40 trees used in the study.
A veterinary researcher wants to compare the effectiveness of three different drenches for controlling worms in sheep. A herd of 60 sheep is used for the experiment and 20 of the sheep are given each drench. One month later, the rate of infestation is determined by faecal examination. The 20 sheep given each drench should be chosen at random from the herd.
A medical researcher is interested in which of 5 drugs for hypertention are most effective at reducing blood pressure. Each of 150 outpatients in a teaching hospital are given one of the drugs and the change in blood pressure is recorded after 1 month. The patients must be randomly given one of the 5 drugs.