# General factorial designs

### Description

This menu covers full factorial designs orthogonal main effects designs for cases for which not all factors are at two levels. Furthermore, Taguchi-parameter designs are covered. This help file is about how and when to apply these.

### Quantitative or Qualitative

Both types of design are suitable for quantitative and qualitative factors alike. If you have quantitative factors only, you may want to consider the special menu for these.

### Full factorial designs

Full factorial designs are straight-forward to generate and are generated by
function `fac.design`

from package DoE.base. The
number of runs needed for a full factorial experiment is the product of the numbers
of levels of all factors. This may be more than is feasible. In such situations, the
orthogonal main effects plans may be helpful. If interactions are also of interest,
it may be useful to combine several plans or to pay attention to specific properties of
orthogonal arrays (automatic support for such possibilities is currently poor and will be improved
in the future).

Full factorial designs can be run in blocks. This is advisable, whenever the experimental
units are not homogeneous, but smaller groups of units (the blocks) can be made
reasonably homogeneous (e.g., batches of material, etc.).

### Orthogonal main effects plans

If a full factorial experiment is too large, an orthogonal main effects plan may be useful. As long as there are no interactions between the factors represented by columns of the array, all such arrays work well, provided they are large enough for stable estimation. Some arrays also work well in the presence of interactions or even allow estimation of interactions for special subsets of variables. However, there is no automated support for selection of an array that has desirable properties. It may therefore be useful to specifically select an array the properties of which are known to the experimenter.

### Warning

Important: For all factorial designs, the experiment must conduct all experimental runs as determined in the design, because the design properties will deteriorate in ways not easily foreseeable, if some combinations are omitted.

It must be carefully considered in the planning phase, whether it is
possible to conduct all experimental runs, or whether there might be restrictions
that do not permit all combinations to be run (e.g.: three factors, each with levels
“small” and “large”, where the combination with all three factors
at level “large” is not doable because of space restrictions).
If such restrictions are encountered, the design should be devised in a different way from the beginning.
If possible, reasonable adjustments to levels should ensure that a factorial design
becomes feasible again. Alternatively, a non-orthogonal D-optimal design can take
the restrictions into account. *Unfortunately, this functionality is not yet implemented in this GUI.*

### Taguchi inner-outer array designs - also called parameter designs

With the menu item *Create Taguchi inner-outer array*, two **existing** designs
can be combined into a crossed inner-outer array design. For more detail, see the
literature and the help in the Taguchi design menu.

### Author(s)

Ulrike Groemping

### References

Box G. E. P, Hunter, W. C. and Hunter, J. S. (2005)
*Statistics for Experimenters, 2nd edition*.
New York: Wiley.

### See Also

See Also `pb`

for the function behind the screening designs,
`FrF2`

for the function behind the regular fractional factorial designs,
and `catlg`

for a catalogue of regular fractional factorial designs,
and `DoEGlossary`

for a glossary of terms relevant in connection with
orthogonal 2-level factorial designs.