In ddarmon/confdist: confdist, a package for creating confidence functions

Wilcox Signed Rank Test

Confidence Distribution

x <- c(207, 397, -63, -213, 96, 203, 442, 247, 70, 64)
minx <- min(x)
maxx <- max(x)

wilcox.test(x, mu = 0)$p.value

wil.conf.dist <- function(mu) wilcox.test(x, mu = mu, alternative = "greater")$p.value

wil.conf.dist <- Vectorize(wil.conf.dist)

curve(wil.conf.dist(mu), xname = "mu", n = 2000, from = min(x), to = max(x))

Confidence Curve

wil.conf.curv <- function(mu) 1 - wilcox.test(x, mu = mu)$p.value

wil.conf.curv <- Vectorize(wil.conf.curv)
par(mfrow = c(1,2))
curve(wil.conf.dist(mu), xname = "mu", n = 2000, from = min(x), to = max(x))
curve(wil.conf.curv(mu), xname = "mu", from = min(x), to = max(x), n = 2000)

Quantile Function

# x <- rnorm(100)

wilcox.test(x, conf.int = TRUE)$conf.int
# wilcox.test(x, conf.int = TRUE, alternative = "less")$conf.int[2]

wil.conf.quant <- function(q) uniroot(function(x) wil.conf.dist(x)-q, lower = minx, upper = maxx)$root

wil.conf.quant.2 <- function(q) wilcox.test(x, conf.int = TRUE, alternative = "less", conf.level = q)$conf.int[2]

wil.conf.quant(.025)
wil.conf.quant(.975)
wil.conf.quant.2(.025)
wil.conf.quant.2(.975)

n <- 100


full.exp <- function(conf.level) {
  x <- rnorm(n)
  range.x <- range(x)
  wil.conf.dist <- function(mu) wilcox.test(x, mu = mu, alternative = "greater")$p.value

wil.conf.dist <- Vectorize(wil.conf.dist)

  wil.conf.quant <- function(q) uniroot(function(x) wil.conf.dist(x)-q, lower = range.x[1], upper = range.x[2])$root

  wil.conf.quant.2 <- function(q) wilcox.test(x, conf.int = TRUE, alternative = "less", conf.level = q)$conf.int[2]

  alpha <- 1 - conf.level
  in.ci.1 <- (0 <= wil.conf.quant(1-alpha/2) && 0 >= wil.conf.quant(alpha/2))

  in.ci.2 <- (0 <= wil.conf.quant.2(1-alpha/2) && 0 >= wil.conf.quant.2(alpha/2))

  return(c(in.ci.1, in.ci.2))
}

full.exp(.95)

counts <- replicate(1000, full.exp(.95))

rowMeans(counts)

for (i in 1:n) {
  if(mean(test.samples[,i]) <= wil.conf.quant(.975) && mean(test.samples[,i]) >= wil.conf.quant(.025)){
    count.uni <- count.uni + 1
  }
}
count.uni/n

count.conf <- 0

for (i in 1:n) {
  if(mean(test.samples[,i]) <= wil.conf.quant.2(.975) && mean(test.samples[,i]) >= wil.conf.quant.2(.025)){
    count.conf <- count.conf + 1
  }
}

count.conf/n

Wilcox Rank Sum

Distribution Function

blue <- lowcarbweights.new
red <- lowfatweights.new

blue <- c(1,2,3,4,5)
red <- c(6,7,8,9,10)

red <- red-4

min.rank.sum <- min(blue) - max(red)

max.rank.sum <- max(blue) - min(red)


wil.rank.sum.conf.dist <- function(mu) wilcox.test(x = blue, y = red, mu = mu, alternative = "greater")$p.value

wil.rank.sum.conf.dist <- Vectorize(wil.rank.sum.conf.dist)

curve(wil.rank.sum.conf.dist(mu), xname = "mu", n = 2000, from = min.rank.sum, to = max.rank.sum)

wil.rank.sum.conf.dist(-20)
wil.rank.sum.conf.dist(-30)

Confidence Curve

wil.rank.sum.conf.curv <- function(mu) 1 - wilcox.test(x = lowcarbweights.new, y = lowfatweights.new, mu = mu)$p.value

wil.rank.sum.conf.curv <- Vectorize(wil.rank.sum.conf.curv)
# par(mfrow = c(1,2))
# curve(wil.rank.sum.conf.dist(mu), xname = "mu", from = -5, to = 5, n = 2000)
curve(wil.rank.sum.conf.curv(mu), xname = "mu", from = min.rank.sum, to = max.rank.sum, n = 2000)

wil.rank.sum.conf.quant <- function(q) uniroot(function(x) wil.rank.sum.conf.dist(x)-q, lower = min.rank.sum, upper = max.rank.sum)$root

wil.rank.sum.conf.quant.2 <- function(q) wilcox.test(x = blue, y = red, conf.int = TRUE, alternative = "less", conf.level = q)$conf.int[2]


wilcox.test(x = blue, y = red, conf.int = TRUE, conf.level = .95)$conf.int


wil.rank.sum.conf.quant(.025)
wil.rank.sum.conf.quant(.975)
wil.rank.sum.conf.quant.2(.025)
wil.rank.sum.conf.quant.2(.975)