Variability
In many experiments, there is little control of the experimental units that are available for use, and they are therefore often very variable.
This variability affects both the design of the experiment and also the analysis that is used to compare the experimental treatments.
Design
Sometimes we have measurements from the experimental units that explain (or partially explain) the differences between them before the experiment is started.
These measurements should be used to group the experimental units into blocks of similar units and a randomised block design should be used.
The design of the experiment should use known differences between the experimental units.
Other measurements called covariates may be made after the experiment has been designed that can also be used to explain variability between the experimental units. (Some authors only use this term to describe numerical characteristics and use the term 'cofactor' for categorical measurements. We use the term covariates for both here.)
Covariates cannot affect the design of the experiment (since their values are unknown before the experiment is designed.
Analysis
Provided the experimental treatments are randomised (either overall or within blocks), the experimental data are analysed in an identical way whatever the design. In all situations,
We should use any available information about the causes of variability in the experimental units to explain variability in the response.
This is done by adding one or more terms to the model for the response and reduces the unexplained variability (the residual sum of squares). The remaining pages in this section give more detail about how this is done.
Reducing unexplained variability makes hypothesis tests more sensitive to differences between the treatments