oacatname, nruns, lineage
and further columns n2 to n72; furthermore, some columns with
calculated metrics are included. name holds the name of the
array, nruns its number of runs, and lineage the way the array can
be constructed from other arrays, if applicable. The columns n2 to n72
each contain the number of factors with the respective number of levels.
The logical columns ff, regular and regular.strict indicate a
full factorial and a regular design in the weak or strict sense (weak: all
SCFT entries are 0 or 1; strict: all ARFT entries are 0 or 1), respectively.
Column SCones contains the number of worst case (=1)
squared canonical correlations; if this number is 0, the design can be considered
to have partial confounding only throughout the entire design.
GR, GRind, maxAR
and maxSC contain the generalized resolution in two versions,
the maximum average R^2 and the maximum squared canonical correlation.
dfe contains the error degrees of freedom of a main effects model,
if all columns of the array are populated; if this is 0, the design is saturated.
A3 to A8 contain the numbers of words of lengths 3 to 8.
More information on these metrics can be found in
generalized.word.length and the literature therein.
The design names also indicate the number of runs and the numbers of factors:
The first portion of each array name (starting with L) indicates the number of runs,
each subsequent pair of numbers indicates a number of levels together with the frequency with which it occurs.
For example, L18.2.1.3.7 is an 18 run design with one factor with
2 levels and seven factors with 3 levels each.
The column lineage deserves particular attention: it is an empty string,
if the design is directly available and can be accessed via its name, or if the design
is a full factorial (e.g. L6.2.1.3.1). Otherwise, the lineage entry is structured as follows:
It starts with the specification of a parent array, given as levels1~no of factors; levels2~no of factors;.
After a colon, there are one or more replacements, each enclosed in brackets; within each pair of brackets,
the left-hand side of the exclamation mark shows the to-be-replaced factor, the right-hand side the
replacement array that has to be used for replacing the levels of such a factor one or more times. For example,
the lineage for L18.2.1.3.7 is 3~6;6~1;:(6~1!2~1;3~1;), which means that the parent array in
18 runs with six 3 level factors and one 6 level factor has to be used, and the 6 level factor has to be replaced
with the full factorial with one 2 level factor and one 3 level factor.generalized.word.length and
examples section below that illustrate this remark.
Cf. also the instructions in section show.oas.
Some of the listed arrays are directly accessible through their names (arrays) or
are full factorials the construction of which is obvious. Others
can be constructed as lineage which is also included as a column
in data frame oacat. Most of the listed arrays have been taken
from Kuhfeld 2009. Exceptions: The three arrays L128.2.15.8.1,
L256.2.19 and L2048.2.63) have been taken from Mee 2009; these
are irregular resolution IV or V arrays for which all main effects can be
orthogonally estimated even in the presence of interactions, or even all 2fis
can be orthogonally estimated, provided there are no higher order effects.
Note that most of the arrays, per default, are guaranteed to orthogonally estimate
all main effects, provided all higher order effects are negligible
(again, the Mee arrays are an exception). This can be
a very severe limitation, of course, and arbitrary strong biases can distort the
estimates even of main effects, if this assumption is violated.
It is therefore strongly recommended to inspect
the quality of an orthogonal array quite closely before deciding to use it
for experimentation. Some functions for inspecting arrays are provided in the
package (cf. generalized.word.length).oa.design for using the designs from oacat in design creation
show.oas for inspecting the available arrays from oacat
generalized.word.length for inspection functions for array properties
arrays for a list of orthogonal arrays which are directly accessible
within the package