Number of possible permutations for a given object
numPerms calculates the maximum number of permutations possible
under the current permutation scheme.
numPerms(object, control = how())
Function numPerms returns the number of permutations for the
passed object and the selected permutation
scheme. object can be one of a data frame, matrix, an object
for which a scores method exists, or a numeric or integer vector. In
the case of a numeric or integer vector, a vector of length 1 can be
used and it will be expanded to a vector of length object
(i.e., 1:object) before computing the number of
permutations. As such, object can be the number of observations
not just the object containing the observations.
The (numeric) number of possible permutations of observations in
object.
In general, mirroring "series" or "grid" designs doubles
or quadruples, respectively, the number of permutations without
mirroring (within levels of strata if present). This is not
true in two special cases:
In "grid" designs where the number of columns is equal
to 2, and
In "series" designs where the number of observations in
a series is equal to 2.
For example, with 2 observations there are 2 permutations for
"series" designs:
1-2, and
2-1.
If these two permutations were mirrored, we would have:
2-1, and
1-2.
It is immediately clear that this is the same set of permutations
without mirroring (if one reorders the rows). A similar situation
arises in "grid" designs where the number of columns
per grid is equal to 2. Note that the number of rows per
grid is not an issue here.
Gavin Simpson
shuffle and
how. Additional nobs methods are
provide, see nobs-methods.
## permutation design --- see ?how ctrl <- how() ## defaults to freely exchangeable ## vector input v <- 1:10 (obs <- nobs(v)) numPerms(v, control = ctrl) ## integer input len <- length(v) (obs <- nobs(len)) numPerms(len, control = ctrl) ## new design, objects are a time series ctrl <- how(within = Within(type = "series")) numPerms(v, control = ctrl) ## number of permutations possible drastically reduced... ## ...turn on mirroring ctrl <- how(within = Within(type = "series", mirror = TRUE)) numPerms(v, control = ctrl) ## Try blocking --- 2 groups of 5 bl <- numPerms(v, control = how(blocks = gl(2,5))) bl ## should be same as pl <- numPerms(v, control = how(plots = Plots(strata = gl(2,5)))) pl stopifnot(all.equal(bl, pl))
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