> spearman_test(Illiteracy~Murder, data=states, distribution=approximate(B=9999))

Approximative Spearman Correlation Test

data: Illiteracy by Murder

Z = 4.7065, p-value < 2.2e-16

alternative hypothesis: true mu is not equal to 0

Based on an approximate permutation test with 9,999 replications, the hypothesis of independence can be rejected. Note that state.x77 is a matrix. It had to be converted into a data frame for use in the coin package.

12.2.4Dependent two-sample and k-sample tests

Dependent sample tests are used when observations in different groups have been matched or when repeated measures are used. For permutation tests with two paired groups, the wilcoxsign_test() function can be used. For more than two groups, use the friedman_test() function.

In chapter 7, we compared the unemployment rate for urban males age 14–24 (U1) with urban males age 35–39 (U2). Because the two variables are reported for each of the 50 US states, you have a two-dependent groups design (state is the matching variable). You can use an exact Wilcoxon signed-rank test to see if unemployment rates for the two age groups are equal:

>library(coin)

>library(MASS)

>wilcoxsign_test(U1~U2, data=UScrime, distribution="exact")

Exact Wilcoxon-Signed-Rank Test

data: y by x (neg, pos) stratified by block

Z = 5.9691, p-value = 1.421e-14

alternative hypothesis: true mu is not equal to 0

Based on the results, you’d conclude that the unemployment rates differ.

12.2.5Going further

The coin package provides a general framework for testing that one group of variables is independent of a second group of variables (with optional stratification on a blocking variable) against arbitrary alternatives, via approximate permutation tests. In particular, the independence_test() function lets you approach most traditional tests from a permutation perspective and create new and novel statistical tests for situations not covered by traditional methods. This flexibility comes at a price: a high level of statistical knowledge is required to use the function appropriately. See the vignettes that accompany the package (accessed via vignette("coin")) for further details.

In the next section, you’ll learn about the lmPerm package. This package provides a permutation approach to linear models, including regression and analysis of variance.