# Resampling Statistics

The coin package provides the ability to perform a wide variety of re-randomization or permutation based statistical tests. These tests do not assume random sampling from well-defined populations. They can be a reasonable alternative to classical procedures when test assumptions can not be met. See coin: A Computational Framework for Conditional Inference for details.

In the examples below, **lower case** letters represent numerical variables and **upper case** letters represent categorical factors. Monte-Carlo simulation are available for all tests. Exact tests are available for 2 group procedures.

## Independent Two- and K-Sample Location Tests

` # Exact Wilcoxon Mann Whitney Rank Sum Test `

# where y is numeric and A is a binary factor

library(coin)

wilcox_test(y~A, data=mydata, distribution="exact")

`# One-Way Permutation Test based on 9999 Monte-Carlo `

# resamplings. y is numeric and A is a categorical factor

library(coin)

oneway_test(y~A, data=mydata,

distribution=approximate(B=9999))

## Symmetry of a response for repeated measurements

`# Exact Wilcoxon Signed Rank Test `

# where y1 and y2 are repeated measures

library(coin)

wilcoxsign_test(y1~y2, data=mydata, distribution="exact")

`# Freidman Test based on 9999 Monte-Carlo resamplings.`

# y is numeric, A is a grouping factor, and B is a

#
blocking factor.

library(coin)

friedman_test(y~A|B, data=mydata,

distribution=approximate(B=9999))

## Independence of Two Numeric Variables

`# Spearman Test of Independence based on 9999 Monte-Carlo`

# resamplings. x and y are numeric variables.

library(coin)

spearman_test(y~x, data=mydata,

distribution=approximate(B=9999))

## Independence in Contingency Tables

`# Independence in 2-way Contingency Table based on`

# 9999 Monte-Carlo resamplings. A and B are factors.

library(coin)

chisq_test(A~B, data=mydata,

distribution=approximate(B=9999))

`# Cochran-Mantel-Haenzsel Test of 3-way Contingency Table`

# based on 9999 Monte-Carlo resamplings. A, B, are
factors

# and C is a stratefying factor.

library(coin)

mh_test(A~B|C, data=mydata,

distribution=approximate(B=9999))

`# Linear by Linear Association Test based on 9999 `

#
Monte-Carlo resamplings.
A and B are ordered factors.

library(coin)

lbl_test(A~B, data=mydata,

distribution=approximate(B=9999))

Many other univariate and multivariate tests are possible using the functions in the **coin **package. See A Lego System for Conditional Inference for more details.

## To Practice

Try the exercises in this course on data analysis and statistical inference in R.