# Nonparametric location tests for one and two samples

## Install required packages

coin

wants <- c("coin")
has   <- wants %in% rownames(installed.packages())
if(any(!has)) install.packages(wants[!has])

## One-sample

### Sign-test

set.seed(123)
medH0 <- 30
DV    <- sample(0:100, 20, replace=TRUE)
DV    <- DV[DV != medH0]
N     <- length(DV)
(obs  <- sum(DV > medH0))
 15
(pGreater <- 1-pbinom(obs-1, N, 0.5))
 0.02069
(pTwoSided <- 2 * pGreater)
 0.04139

### Wilcoxon signed rank test

IQ    <- c(99, 131, 118, 112, 128, 136, 120, 107, 134, 122)
medH0 <- 110
wilcox.test(IQ, alternative="greater", mu=medH0, conf.int=TRUE)

Wilcoxon signed rank test

data:  IQ
V = 48, p-value = 0.01855
alternative hypothesis: true location is greater than 110
95 percent confidence interval:
113.5   Inf
sample estimates:
(pseudo)median
121 

## Two independent samples

### Sign-test

Nj  <- c(20, 30)
DVa <- rnorm(Nj, mean= 95, sd=15)
DVb <- rnorm(Nj, mean=100, sd=15)
wIndDf <- data.frame(DV=c(DVa, DVb),
IV=factor(rep(1:2, Nj), labels=LETTERS[1:2]))

Looks at the number of cases in each group which are below or above the median of the combined data.

library(coin)
median_test(DV ~ IV, distribution="exact", data=wIndDf)

Exact Median Test

data:  DV by IV (A, B)
Z = 1.143, p-value = 0.3868
alternative hypothesis: true mu is not equal to 0 

### Wilcoxon rank-sum test ($=$ Mann-Whitney $U$-test)

wilcox.test(DV ~ IV, alternative="less", conf.int=TRUE, data=wIndDf)

Wilcoxon rank sum test

data:  DV by IV
W = 202, p-value = 0.02647
alternative hypothesis: true location shift is less than 0
95 percent confidence interval:
-Inf -1.771
sample estimates:
difference in location
-9.761 
library(coin)
wilcox_test(DV ~ IV, alternative="less", conf.int=TRUE,
distribution="exact", data=wIndDf)

Exact Wilcoxon Mann-Whitney Rank Sum Test

data:  DV by IV (A, B)
Z = -1.941, p-value = 0.02647
alternative hypothesis: true mu is less than 0
95 percent confidence interval:
-Inf -1.771
sample estimates:
difference in location
-9.761 

## Two dependent samples

### Sign-test

N      <- 20
DVpre  <- rnorm(N, mean= 95, sd=15)
DVpost <- rnorm(N, mean=100, sd=15)
wDepDf <- data.frame(id=factor(rep(1:N, times=2)),
DV=c(DVpre, DVpost),
IV=factor(rep(0:1, each=N), labels=c("pre", "post")))
medH0  <- 0
DVdiff <- aggregate(DV ~ id, FUN=diff, data=wDepDf)
(obs   <- sum(DVdiff\$DV < medH0))
 7
(pLess <- pbinom(obs, N, 0.5))
 0.1316

### Wilcoxon signed rank test

wilcoxsign_test(DV ~ IV | id, alternative="greater",
distribution="exact", data=wDepDf)

Exact Wilcoxon-Signed-Rank Test

data:  y by x (neg, pos)
stratified by block
Z = 2.128, p-value = 0.01638
alternative hypothesis: true mu is greater than 0 

## Detach (automatically) loaded packages (if possible)

try(detach(package:coin))
try(detach(package:modeltools))
try(detach(package:survival))
try(detach(package:mvtnorm))
try(detach(package:splines))
try(detach(package:stats4))