# bootstrap

From resample v0.4
by Tim Hesterberg

##### One and two sample bootstrap sampling and permutation tests.

Basic resampling. Supply the data and statistic to resample.

- Keywords
- htest, nonparametric

##### Usage

```
bootstrap(data, statistic, R = 10000,
args.stat = NULL, seed = NULL, sampler = samp.bootstrap,
label = NULL, statisticNames = NULL, block.size = 100,
trace = FALSE)
bootstrap2(data, statistic, treatment, data2 = NULL, R = 10000,
ratio = FALSE,
args.stat = NULL, seed = NULL, sampler = samp.bootstrap,
label = NULL, statisticNames = NULL, block.size = 100,
trace = FALSE)
permutationTest(data, statistic, R = 9999,
alternative = "two.sided", resampleColumns = NULL,
args.stat = NULL, seed = NULL, sampler = samp.permute,
label = NULL, statisticNames = NULL, block.size = 100,
trace = FALSE, tolerance = .Machine$double.eps ^ 0.5)
permutationTest2(data, statistic, treatment, data2 = NULL, R = 9999,
alternative = "two.sided", ratio = FALSE, paired = FALSE,
args.stat = NULL, seed = NULL, sampler = samp.permute,
label = NULL, statisticNames = NULL, block.size = 100,
trace = FALSE, tolerance = .Machine$double.eps ^ 0.5)
```

##### Arguments

- data
- vector, matrix, or data frame.
- statistic
- a function, or expression (e.g.
`mean(myData, trim = .2)`

. - R
- number of replicates (bootstrap samples or permutation resamples).
- treatment
- a vector with two unique values.
For two-sample applications, suppy either
`treatment`

or`data2`

. - data2
- an object like
`data`

; the second sample. - alternative
- one of
`"two.sided"`

,`"greater"`

, or`"less"`

. If`statistic`

returns a vector, this may be a vector of the same length. - ratio
- logical, if
`FALSE`

then statistics for two samples are combined using statistic1 - statistic2 (the statistics from the two samples). If`TRUE`

, it uses statistic1 / statistic2. - resampleColumns
- integer, or character (a subset of the column names of
`data`

); if supplied then only these columns of the data are permuted. For example, for a permutation test of the correlation of x and y, only one of the variables should be per - args.stat
- a list of additional arguments to pass to
`statistic`

, if it is a function. - paired
- logical, if
`TRUE`

then observations in`data`

and`data2`

are paired, and permutations are done within each pair. Not yet implemented. - seed
- old value of .Random.seed, or argument to set.seed.
- sampler
- a function for resampling, see
`help(samp.bootstrap)`

. - label
- used for labeling plots (in a future version).
- statisticNames
- a character vector the same length as the vector returned by
`statistic`

. - block.size
- integer. The
`R`

replicates are done this many at a time. - trace
- logical, if
`TRUE`

an indication of progress is printed. - tolerance
- when computing P-values, differences smaller than
`tolerance`

(absolute or relative) between the observed value and the replicates are considered equal.

##### Details

There is considerable flexibility in how you specify the data and statistic.

For the `statistic`

, you may supply a function, or an expression.
For example, if `data = x`

, you may specify any of

`statistic = mean`

`statistic = mean(x)`

`statistic = mean(data)`

##### Value

- a list with class
`"bootstrap"`

,`"bootstrap2"`

,`"permutationTest"`

, or`"permutationTest2"`

, that inherits from`"resample"`

, with components: observed the value of the statistic for the original data. replicates a matrix with `R`

rows and`p`

columns.n number of observations in the original data, or vector of length 2 in two-sample problems. p `length(observed)`

.R number of replications. seed the value of the seed at the start of sampling. call the matched call. statistics a data frame with `p`

rows, with columns`"observed"`

,`"mean"`

(the mean of the replicates), and other columns appropriate to resampling; e.g. the bootstrap objects have columns`"SE"`

and`"Bias"`

, while the permutation test objects have`"Alternative"`

and`"PValue"`

.- The two-sample versions have an additional component:
resultsBoth containing resampling results from each data set. containing two components, the results from resampling each of the two samples. These are `bootstrap`

objects; in the`permutationTest2`

case they are the result of sampling without replacement.- There are functions for printing and plotting these objects,
in particular
`print`

,`hist`

,`qqnorm`

,`plot`

(currently the same as`hist`

),`quantile`

.

##### code

`data2`

##### itemize

`statistic = colMeans(data)`

##### item

`statistic = mean(myData$x)`

`statistic = mean(myData[, "x"])`

##### See Also

##### Examples

```
# See full set of examples in resample-package, including different
# ways to call the functions depending on the structure of the data.
data(Verizon)
CLEC <- with(Verizon, Time[Group == "CLEC"])
bootC <- bootstrap(CLEC, mean)
bootC
hist(bootC)
qqnorm(bootC)
```

*Documentation reproduced from package resample, version 0.4, License: BSD_3_clause + file LICENSE*

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