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.

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