One and Two Sample Permutation Test
Performs the permutation test for the one and two sample problem.
## Default S3 method:
perm.test(x, y, paired=FALSE, alternative=c("two.sided", "less", "greater"),
mu=0, exact=NULL, conf.int=FALSE, conf.level=0.95, tol=NULL, ...)
## S3 method for class 'formula'
perm.test(formula, data, subset, na.action, ...)x |
numeric vector of integer data values. |
y |
numeric vector of integer data values. |
paired |
a logical indicating whether you want a paired test. |
alternative |
the alternative hypothesis must be
one of |
mu |
a number specifying an optional location parameter. |
exact |
a logical indicating whether an exact p-value should be computed. |
conf.int |
a logical indicating whether a confidence interval should be computed. |
conf.level |
confidence level of the interval. |
tol |
real. real valued scores are mapped into integers by
multiplication. Make sure that the absolute difference between
the "true" quantile and the approximated quantile is less
than |
formula |
a formula of the form |
data |
an optional data frame containing the variables in the model 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 |
... |
further arguments to be passed to or from methods. |
The permutation test is performed for integer valued observations or
scores. If real values x or y are passed to this function
the following applies: if exact is true (i.e. the sample size is
less than 50 observations) and tol is not given, the scores are
mapped into \{1,…,N\}, see pperm for the details.
Otherwise the p-values are computed using tol. If the sample size
exceeds $50$ observations, the usual normal approximation is used.
P-values are computed according to the StatXact-manual, see
pperm.
For (in principle) continuous variables the confidence sets represent the "largest shift in location being consistent with the observations". For discrete variables with only a few categories they are hard to interpret. In the case of binary data (e.g. success / failure) the confidence sets can be interpreted as the differences of two success-rates covered by the data. For a detailed description see R\"ohmel (1996).
Confidence intervals are only available for independent samples. When the
sample sizes are unbalanced, length(x) needs to be smaller than
length(y).
A list with class "htest" containing the following components:
statistic |
the value of the test statistic with a name describing it. |
p.value |
the p-value for the test. |
pointprob |
this gives the probability of observing the test statistic itself. |
null.value |
the location parameter |
alternative |
a character string describing the alternative hypothesis. |
method |
the type of test applied. |
data.name |
a character string giving the names of the data. |
conf.int |
a confidence interval for the location parameter.
(Only present if argument |
Confidence intervals may need some cpu-time ...
Torsten Hothorn <Torsten.Hothorn@rzmail.uni-erlangen.de>
Joachim R\"ohmel (1996), Precision intervals for estimates of the difference in success rates for binary random variables based on the permutation principle. Biometrical Journal, 38(8), 977–993.
Cyrus R. Mehta & Nitin R. Patel (2001), StatXact-5 for Windows. Manual, Cytel Software Cooperation, Cambridge, USA
# Example from Gardner & Altman (1989), p. 30 # two treatments A and B, 1 means improvement, 0 means no improvement # confidence sets cf. R\"ohmel (1996) A <- c(rep(1, 61), rep(0, 19)) B <- c(rep(1, 45), rep(0, 35)) perm.test(A, B, conf.int=TRUE, exact=TRUE) # one-sample AIDS data (differences only), Methta and Patel (2001), # Table 8.1 page 181 data(sal) attach(sal) ppdiff <- pre - post detach(sal) # p-values in StatXact == 0.0011 one-sided, 0.0021 two.sided, page 183 perm.test(ppdiff) perm.test(ppdiff, alternative="less") perm.test(ppdiff, exact=FALSE)
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