R: Basic information for orthogonal main effects designs

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Basic information for orthogonal main effects designs

Description

Basic information for orthogonal main effects design Menu

Details

It is useful to look at available designs for deciding which specific design should be selected. For example, when trying to automatically optimize a design, it may be more useful to start from a design with relatively few factors. If a design for two 2-level factors, one 4-level factor and one 8-level factor is sought, you may e.g. use the array L64.2.5.4.10.8.4 or the array L64.2.53.4.1.8.1, which will make quite a difference in terms of run time for the optimization choice “min34”.

The designs L128.2.15.8.1, L256.2.19 and L2048.2.63 are irregular resolution V designs for the 2-level factors.

Brief statistical background

The orthogonal main effects designs are of different types. They all work well if there are indeed no interactions between factors. Some of them have complete aliasing between main effects and two-factor interactions at least for some factors. It is therefore advisable to check the design before actually conducting the experiment with respect to its potential analysis options and biases.

Note that it is usually preferable to create an experiment with solely 2-level factors from the special menu for 2-level situations (exceptions: resolution V nonregular arrays in 128, 256 or 2048 runs, cf. Details section). If there is just one factor at more than 2 levels, it may also be useful to simply cross this factor with an otherwise 2-level design.

If only relatively few of the columns are used, it is possible with some orthogonal arrays to also estimate interactions, or at least to estimate main effects unbiasedly even in the presence of interactions. This may e.g. be possible for some of the arrays in 2, 4 and 8 or 16 level factors (that have arisen from regular fractional factorials). Automatic optimization can help finding such designs.

It is highly recommended to diagnose the structure of the design before using it for experimentation, e.g. using the “Summarize design ...” item in the “Inspect design” menu.

Inputs on Tab Base Settings

name of design: must be a valid name. The design itself is created under this name in the R workspace.
number of factors: must always be specified. The number of factors must match the number of entries on the Factor Details tab.
specific array: can be selected from the drop-down list; this implies that this particular array is used for generating the design; the array name indicates its number of runs and the maximum possible numbers of factors with various numbers of levels. For example, the array L12.2.2.6.1 can accomodate 2 factors at 2 levels each and one factor at 6 levels
Automatic optimization: can be selected from the drop-down list. The default is no optimization (“none”). “min3” requests minimization of generalized words of length 3 (cf. generalized.word.length), while “min34” requests further optimization among several equally-good length 3 designs w.r.t. length 4 words. Automatic optimization may sometimes take very long or use up too many resources; usability will be better for designs with fewer factors (cf. also details section).
minimum number of runs: can be selected from dropdown, but is not needed
minimum residual df: is per default 0 and can be set to any positive integer number; it specifies the minium number of extra runs over and above what would be needed for a model with main effects for all factors; for example, when using the design L12.2.2.6.1 for two 2-level factors and one 6-level factor, the model with all main effects requires 1+2*(2-1)+1*(6-1)=8 degrees of freedom, i.e. there are four extra degrees of freedom for pure error or lack of fit
replications: is the number of times each experimental run is conducted. If larger than 1, each run is conducted several times. If the checkbox next to the number of replications is checked, it is assumed that the experiment involves repeated measurements for one setup of the experimental run; if it is not checked, the experimental run itself is replicated with everything relevant newly set up (much more valuable than repeated measurements, unless the key driver of variability is in the measuring step). If the check box is not checked, the experiment will be randomized separately for each round of replications (first all first runs, then all second runs etc.).
randomization settings: should normally not be changed; you can provide a seed if you want to exactly reproduce a randomized design created in the past. Unchecking the randomization box will produce a non-randomized experiment. This is usually NOT recommended.
Inspect available designs: based on requests on the number of runs (from, to) and decisions whether or not child arrays are to be shown, and whether to only display designs that can accomodate factors with the factor level settings from the “Factor Details” tab. The button will create a printout of the available designs, based on the work horse function show.oas. The menu remains open and needs to be maximized again after looking at the displayed designs.

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