compare.2.vectors: Compare two vectors using various tests.

Description

Compares two vectors x and y using t-test, Welch-test (also known as Satterthwaite), Wilcoxon-test, and a permutation test implemented in coin.

Usage

compare.2.vectors(x, y, paired = FALSE, na.rm = FALSE, 
     tests = c("parametric", "nonparametric"), coin = TRUE, 
     alternative = "two.sided", 
     perm.distribution, 
     wilcox.exact = NULL, wilcox.correct = TRUE)

Value

a list with up to two elements (i.e., paramteric and/or nonparamteric) each containing a data.frame with the following columns: test, test.statistic, test.value, test.df, p.

Arguments

x: a (non-empty) numeric vector of data values.
y: a (non-empty) numeric vector of data values.
paired: a logical whether the data is paired. Default is FALSE.
na.rm: logical. Should NA be removed? Default is FALSE.
tests: Which tests to report, parametric or nonparamteric? The default c("parametric", "nonparametric") reports both. See details. (Arguments may be abbreviated).
coin: logical or character. Should (permutation) tests from the coin package be reported? Default is TRUE corresponding to all implemented tests. FALSE calculates no tests from coin. A character vector may include any of the following (potentially abbreviated) implemented tests (see also Details): c("permutation", "Wilcoxon", "median")
alternative: a character, the alternative hypothesis must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter, will be passed to all functions.
perm.distribution: distribution argument to coin, see NullDistribution or , IndependenceTest. If missing, defaults to coin::approximate(100000) indicating an approximation of the excat conditional distribution with 100.000 Monte Carlo samples. One can use "exact" for small samples and if paired = FALSE.
wilcox.exact: exact argument to wilcox.test.
wilcox.correct: correct argument to wilcox.test.

Details

The parametric tests (currently) only contain the t-test and Welch/Statterwaithe/Smith/unequal variance t-test implemented in t.test. The latter one is only displayed if paired = FALSE.

The nonparametric tests (currently) contain the Wilcoxon test implemented in wilcox.test (stats::Wilcoxon) and (if coin = TRUE) the following tests implemented in coin:

a permutation test oneway_test (the only test in this selction not using a rank transformation),
the Wilcoxon test wilcox_test (coin::Wilcoxon), and
the median test median_test.

Note that the two implementations of the Wilcoxon test probably differ. This is due to differences in the calculation of the Null distributions.

Examples

Run this code


with(sleep, compare.2.vectors(extra[group == 1], extra[group == 2]))

# gives:
## $parametric
##    test test.statistic test.value test.df       p
## 1     t              t     -1.861   18.00 0.07919
## 2 Welch              t     -1.861   17.78 0.07939
## 
## $nonparametric
##              test test.statistic test.value test.df       p
## 1 stats::Wilcoxon              W     25.500      NA 0.06933
## 2     permutation              Z     -1.751      NA 0.08154
## 3  coin::Wilcoxon              Z     -1.854      NA 0.06487
## 4          median              Z     -1.744      NA 0.17867

# compare with:
with(sleep, compare.2.vectors(extra[group == 1], extra[group == 2], 
                              alternative = "less"))

with(sleep, compare.2.vectors(extra[group == 1], extra[group == 2], 
                              alternative = "greater"))

# doesn't make much sense as the data is not paired, but whatever:
with(sleep, compare.2.vectors(extra[group == 1], extra[group == 2], 
                              paired = TRUE))

# from ?t.test:
compare.2.vectors(1:10,y=c(7:20, 200))