Experiments with many factors
In a complete factorial experiment, the number of possible treatment combinations in a factorial experiment increases very quickly as the number of controlled factors increases, as illustrated in the table below.
Number of factors, k | |||||||
---|---|---|---|---|---|---|---|
2 | 3 | 4 | 5 | 6 | |||
Levels per factor | 2 | 4 | 8 | 16 | 32 | 64 | 2k |
3 | 9 | 27 | 81 | 243 | 729 | 3k |
Factors with two levels
To keep the number of experimental units to a practical level, experiments involving many factors are usually conducted with only two levels for each factor. If each of k factors in a complete factorial experiment has two levels, the experiment is called a 2k factorial experiment.
This section describes complete 2k factorial experiments that use 2k experimental units.
We use this section to introduce notation and concepts for factorial experiments with 2-level factors. However there are often insufficient resources to permit even a single replicate of such an experiment, so incomplete designs are often used.
The next section will describe the design and analysis of incomplete experiments for 2-level factors.