## Documentation Center |

On this page… |
---|

To systematically vary experimental factors, assign each factor
a discrete set of *levels*.
Full factorial designs measure response variables using every *treatment* (combination of the factor
levels). A full factorial design for *n* factors
with *N*_{1},
..., *N*_{n} levels requires *N*_{1} ×
... × *N*_{n} experimental runs—one for each treatment. While
advantageous for separating individual effects, full factorial designs
can make large demands on data collection.

As an example, suppose a machine shop has three machines and
four operators. If the same operator always uses the same machine,
it is impossible to determine if a machine or an operator is the cause
of variation in production. By allowing every operator to use every
machine, effects are separated. A full factorial list of treatments
is generated by the Statistics Toolbox™ function `fullfact`:

dFF = fullfact([3,4]) dFF = 1 1 2 1 3 1 1 2 2 2 3 2 1 3 2 3 3 3 1 4 2 4 3 4

Each of the 3×4 = 12 rows of `dFF` represent
one machine/operator combination.

Many experiments can be conducted with two-level factors, using *two-level designs*. For example,
suppose the machine shop in the previous example always keeps the
same operator on the same machine, but wants to measure production
effects that depend on the composition of the day and night shifts.
The Statistics Toolbox function `ff2n` generates
a full factorial list of treatments:

dFF2 = ff2n(4) dFF2 = 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1

Each of the 2^{4} = 16 rows of `dFF2` represent
one schedule of operators for the day (`0`) and night
(`1`) shifts.

Was this topic helpful?