# Analyze experimental designs

### Description

This is a brief explanation on the analysis facilities for experimental designs in the Analyze Design menu.

### Available analysis options

**Generally applicable analysis options**
The topmost menu entry Default linear model is of interest for all design types
and is usable whenever the active dataset is a design with response.
However, the default linear model analysis does not work for long version designs
with repeated measurements or for parameter designs in long format,
as it usually does not make sense in such situations.
Rather, such designs should be brought into wide format by using the
Design –> Combine or Modify Designs –> Change from long to wide format
menu.

Note that the default linear model analysis is a quick first shot that should often be tuned and sometimes (e.g. in many cases splitplot designs) replaced by a different analysis strategy for serious modelling. Tuning can be done by using the built-in linear model functions from the R-Commander Analyze menu. The R-Commander Models menu also offers interesting options for subsequent model diagnostics and graphics.

**Analysis options for general factorial designs**

For a general factorial design with a response, main effects and interaction plots
can be generated (one at a time) by a menu which was slightly from Rcmdrs general
menu for graphing arithmetic means.

**Analysis options specific to 2-level designs**

There are two types of orthogonal 2-level factorial designs,
regular fractional factorial designs and screening designs.
The latter has more interesting analysis options than the former.

Effects plots and main effects plots are of interest for both types of 2-level designs alike, while interaction plots are usually of interest for the regular designs only.

Note that the interpretation of all effects plots, main effects and interaction plots
is useful only in connection with knowledge about the alias structure of a design.
For regular designs, this can e.g. be obtained from the *Summarize design*
menu item within the *Inspect design* sub menu of the *Design* menu.
For screening designs, if it can be assumed that interactions are likely to be
much less important than main effects, the main effect plots may be interpretable
without such thoughts. Considerations involving the interactions become quite complicated
with screening designs because of partial aliasing.
Advanced users might also want to try the Bayesian methods
offered in package `BsMD-package`

, which are currently not implemented
in RcmdrPlugin.DoE.

**Analysis options specific to designs with quantitative factors**

are available within R-package rsm
and are implemented in particular for response surface designs; they can also
be used for other designs with quantitative variables, especially for latin hypercube
designs. (However, for the latter, there are often reasons to use nonparametric approaches.

The menu item *Response surface model ...* creates a response surface
analysis with first order (FO) terms, and potentially also two-factor interactions
(TWI) and/or pure quadratic (PQ) terms. The resulting object has class `rsm`

and can be postprocessed with the subsequent menu items.

The menu item *Steepest slope ...* supports moving the experimental range
towards a more promising area, based on a first order model or on a second order
model with a saddle point.

The menu item *Plot response surface ...* supports creation of contour,
perspective or image plots of a response surface model,
and can also be used for linear models with quantitative variables.

**General analysis functionality from R Commander **

It is of course also possible to use other analysis facilities within the R Commander,
or to use the command-line facilities offered in package `rsm`

and elsewhere.

### 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 `summary.design`

for
how designs are summarized, `formula.design`

for the function that creates the default linear model formula, or
`DanielPlot`

, `MEPlot`

and `IAPlot`

for the functions behind the graphical analysis tools for 2-level factors.