MC.test: Monte Carlo hypothesis testing for two samples.

In asbio: A Collection of Statistical Tools for Biologists

Monte Carlo hypothesis testing for two samples.

Description

MC.test calculates a permutation distribution of test statistics from a Welcht-test. It compares this distribution to an initial test statistic calculated using non-permuted data, to derive an empirical P-value.

Usage

MC.test(Y,X, perm = 1000, alternative = "not.equal", paired = FALSE, print = TRUE)

Arguments

Y	Response data.
X	Categorical explanatory variable.
perm	Number of iterations.
paired	Logical: Are sample paired?
alternative	Alternative hypothesis. One of three options: "less","greater", or "not.equal". These provide lower-tail, upper-tail, and two-tailed tests.
print	Logical: automatically print a pretty summary of results (default).

Details

The method follows the description of Manly (1998) for a two-sample test. Upper and lower tailed tests are performed by finding the portion of the distribution greater than or equal to the observed t test statistic (upper-tailed) or less than or equal to the observed test statistic (lower-tailed). A two tailed test is performed by multiplying the portion of the null distribution greater than or equal to the absolute value of the observed test statistic and less than or equal to the absolute value of the observed test statistic times minus one. Results from the test will be similar to oneway_test from the library coin because it is based on an equivalent test statistic. As with t.test, pairing is assumed to occur within levels of X. That is, the responses Y = 11 and Y = 2 occur in the same pair (block) below.

Y <- c(11,12,13,2,3,4)

X <- c(1,1,1,2,2,2)

Value

Returns a list with the following items:

observed.test.statistic	t-statistic calculated from non-permuted (original)data.
no_of_permutations_exceeding_observed_value	The number of times a Monte Carlo derived test statistic was more extreme than the initial observed test statistic.
p.value	Empirical P-value
alternative	The alternative hypothesis

Author(s)

Ken Aho, thanks to Vince Buonaccorsi who found an error under paired = TRUE.

References

Manly, B. F. J. (1997) Randomization and Monte Carlo Methods in Biology, 2nd edition. Chapman and Hall, London.

See Also

t.test

Examples

Y<-c(runif(100,1,3),runif(100,1.2,3.2))
X<-factor(c(rep(1,100),rep(2,100)))
MC.test(Y,X,alternative="less")

asbio documentation built on May 29, 2024, 5:57 a.m.