perm.test: Permutation Test
In jmuOutlier: Permutation Tests for Nonparametric Statistics

Description Usage Arguments Details Value Note Author(s) References Examples

Performs one-sample and two-sample permutation tests on vectors of data.

1 2	perm.test(x, y = NULL, alternative = c("two.sided", "less", "greater"), mu = 0, paired = FALSE, all.perms = TRUE, num.sim = 20000, plot = FALSE, stat = mean, ...)

`x`	A (non-empty) numeric vector of data values.
`y`	An optional numeric vector data values.
`alternative`	A character string specifying the alternative hypothesis, and must be one of `"two.sided"` (default), `"greater"` or `"less"`. Only the initial letter needs to be specified.
`mu`	A number indicating the null value of the location parameter (or the difference in location parameters if performing a two-sample test).
`paired`	Logical, indicating whether or not a two-sample test should be paired, and is ignored for a one-sample test.
`all.perms`	Logical. The exact p-value is attempted when `all.perms` (i.e., all permutations) is `TRUE` (default), and is simulated when `all.perms` is `FALSE` or when computing an exact p-value requires more than `num.sim` calculations.
`num.sim`	The upper limit on the number of permutations generated.
`plot`	Logical. If `TRUE`, then plot the histogram of the permutation distribution; otherwise, list the p-value.
`stat`	Function, naming the test statistic, such as `mean` and `median`.
`...`	Optional arguments to `stat`; and is the second argument to `stat` when unspecified. For example, if `stat` equals `mean`, then the second argument `trim` denotes the fraction (0 to 0.5) of observations to be trimmed from each end of `x` and `y` before the mean is computed.

A paired test using data x and nonNULL y is equivalent to a one-sample test using data x-y. The output states more details about the permutation test, such as one-sample or two-sample, and whether or not the p.value calculated was based on all permutations.

`alternative`	Same as the input.
`mu`	Same as the input.
`p.value`	The p-value of the permutation test.

The formulas computed within perm.test are based on the textbook by Higgins (2004).

Steven T. Garren, James Madison University, Harrisonburg, Virginia, USA

Higgins, J. J. (2004) Introduction to Modern Nonparametric Statistics.

# One-sample test

print( x <- rnorm(10,0.5) ) 

perm.test( x, stat=median )

# Two-sample unpaired test

print( y <- rnorm(13,1) )

perm.test( x, y )

 [1]  1.6013242  1.5846410 -0.5714917  0.3988142  0.5416978  1.3851507
 [7] -0.2418826  1.3553764  0.5802484 -0.4113348
[[1]]
[1] "One-sample permutation test was performed."

[[2]]
[1] "p-value was calculated based on all permutations."

$alternative
[1] "two.sided"

$mu
[1] 0

$p.value
[1] 0.078125

 [1]  1.5735208  1.5312516  0.4463142  1.2528721 -0.5620620  2.3429980
 [7]  0.7756172  1.6497653  0.7889176  0.5107436  0.7542697  1.4606170
[13]  0.4759810
[[1]]
[1] "Unpaired two-sample permutation test was performed."

[[2]]
[1] "p-value was estimated based on 20000 simulations."

$alternative
[1] "two.sided"

$mu
[1] 0

$p.value
[1] 0.2584