# 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.