Analysing experimental data
After the experiment has been conducted, the resulting data must be analysed
to estimate and test the effects of the controlled variables.
These estimates and tests are based on a statistical model
for the response that explains how its value varies between the experimental
units.
Reasons for variability in the response
In experimental data, there are three potential reasons for variability in
the response.
- Different values of the controlled variables
- Changing the value of a factor can result in changes to
the response. The purpose of the experiment is to assess the magnitude of
these changes. This is called explained variation since
it can be explained in terms of the explanatory factors.
- Understood differences between the experimental units
- The design of many experiments makes use of known differences between the experimental units. For example, they may be grouped into blocks of similar units; some of the variation in the response may be associated with such blocks. The variation in the response associated with this known structure of the experimental units is also explained variation.
- Other differences between the experimental units
- There is usually natural variability between the experimental units and
in the measurement process. Two response measurements with the same values
for the explanatory variables will usually differ. This natural variability
cannot be explained in terms of the controlled variables and is called unexplained
variation.
The difference between the first two components of variation is important but:
The distinction between explained and unexplained variation is critically important.