Basic information for orthogonal main effects design Menu
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.
must be a valid name. The design itself is created under this name in the R workspace.
must always be specified. The number of factors must match the number of entries on the Factor Details tab.
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
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).
can be selected from dropdown, but is not needed
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
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.).
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.
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.
Ulrike Groemping
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.
See Also oa.design for the function that does the calculations
and Menu.General for overall help on the general factorial design menu.