perm.t.test: Permutation t-Test

In MKinfer: Inferential Statistics

Permutation t-Test

Description

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

Usage

perm.t.test(x, ...)

## Default S3 method:
perm.t.test(x, y = NULL,
       alternative = c("two.sided", "less", "greater"),
       mu = 0, paired = FALSE, var.equal = FALSE,
       conf.level = 0.95, R = 9999, symmetric = TRUE, ...)

## S3 method for class 'formula'
perm.t.test(formula, data, subset, na.action, ...)

Arguments

x	a (non-empty) numeric vector of data values.
y	an optional (non-empty) numeric vector of data values.
alternative	a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter.
mu	a number indicating the true value of the mean (or difference in means if you are performing a two sample test).
paired	a logical indicating whether you want a paired t-test.
var.equal	a logical variable indicating whether to treat the two variances as being equal. If TRUE then the pooled variance is used to estimate the variance otherwise the Welch (or Satterthwaite) approximation to the degrees of freedom is used.
conf.level	confidence level of the interval.
R	number of (Monte-Carlo) permutations.
symmetric	a logical variable indicating whether to assume symmetry in the two-sided test. If TRUE then the symmetric permutation p value otherwise the equal-tail permutation p value is computed.
formula	a formula of the form lhs ~ rhs where lhs is a numeric variable giving the data values and rhs a factor with two levels giving the corresponding groups.
data	an optional matrix or data frame (or similar: see model.frame) containing the variables in the formula formula. By default the variables are taken from environment(formula).
subset	an optional vector specifying a subset of observations to be used.
na.action	a function which indicates what should happen when the data contain NAs. Defaults to getOption("na.action").
...	further arguments to be passed to or from methods.

Details

The implemented test corresponds to the proposal of Chapter 15 of Efron and Tibshirani (1993) for equal variances as well as Janssen (1997) respectively Chung and Romano (2013) for unequal variances.

The function returns permutation p values and confidence intervals as well as the results ot the t-test without permutations.

The formula interface is only applicable for the 2-sample tests.

alternative = "greater" is the alternative that x has a larger mean than y.

If paired is TRUE then both x and y must be specified and they must be the same length. Missing values are silently removed (in pairs if paired is TRUE). If var.equal is TRUE then the pooled estimate of the variance is used. By default, if var.equal is FALSE then the variance is estimated separately for both groups and the Welch modification to the degrees of freedom is used.

If the input data are effectively constant (compared to the larger of the two means) an error is generated.

Value

A list with class "perm.htest" (derived from class htest) containing the following components:

statistic	the value of the t-statistic.
parameter	the degrees of freedom for the t-statistic.
p.value	the p-value for the test.
perm.p.value	the (Monte-Carlo) permutation p-value for the test.
conf.int	a confidence interval for the mean appropriate to the specified alternative hypothesis.
perm.conf.int	a (Monte-Carlo) permutation percentile confidence interval for the mean appropriate to the specified alternative hypothesis.
estimate	the estimated mean or difference in means depending on whether it was a one-sample test or a two-sample test.
perm.estimate	(Monte-Carlo) permutation estimate.
null.value	the specified hypothesized value of the mean or mean difference depending on whether it was a one-sample test or a two-sample test.
stderr	the standard error of the mean (difference), used as denominator in the t-statistic formula.
perm.stderr	(Monte-Carlo) permutation standard error.
alternative	a character string describing the alternative hypothesis.
method	a character string indicating what type of t-test was performed.
data.name	a character string giving the name(s) of the data.

Note

Code and documentation are for large parts identical to function t.test.

References

B. Efron, R.J. Tibshirani. An Introduction to the Bootstrap. Chapman and Hall/CRC 1993.

A. Janssen (1997). Studentized permutation tests for non-i.i.d, hypotheses and the generalized Behrens-Fisher problem. Statistics and Probability Letters, 36, 9-21.

E. Chung, J.P. Romano (2013). Exact and asymptotically robust permutation tests. The Annals of Statistics, 41(2), 484-507.

See Also

t.test, meanCI, meanDiffCI, boot.t.test

Examples

require(graphics)

t.test(1:10, y = c(7:20))      # P = .00001855
perm.t.test(1:10, y = c(7:20))

t.test(1:10, y = c(7:20, 200)) # P = .1245    -- NOT significant anymore
perm.t.test(1:10, y = c(7:20, 200)) # perm.conf.int affected by outlier!


## Classical example: Student's sleep data
plot(extra ~ group, data = sleep)
## Traditional interface
with(sleep, t.test(extra[group == 1], extra[group == 2]))
with(sleep, perm.t.test(extra[group == 1], extra[group == 2]))
## Formula interface
t.test(extra ~ group, data = sleep)
perm.t.test(extra ~ group, data = sleep)

MKinfer documentation built on April 17, 2023, 9:10 a.m.