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.