Bootstrapped p-value for a correlation coefficient on R

Question

On R, I used the boostrap method to get a correlation coefficient estimation and the confidence intervals. To get the p-value, I thought, I can calculate the p

Answer 1

The standard way of bootstrapping in R is to use base package boot. You start by defining the bootstrap function, a function that takes two arguments, the dataset and an index into the dataset. This is function bootCorTest below. In the functionyou subset the dataset selecting just the rows defined by the index.

The rest is straightforward.

library(boot)

bootCorTest <- function(data, i){
    d <- data[i, ]
    cor.test(d$x, d$y)$p.value
}


# First dataset in help("cor.test")
x <- c(44.4, 45.9, 41.9, 53.3, 44.7, 44.1, 50.7, 45.2, 60.1)
y <- c( 2.6,  3.1,  2.5,  5.0,  3.6,  4.0,  5.2,  2.8,  3.8)
dat <- data.frame(x, y)

b <- boot(dat, bootCorTest, R = 1000)

b$t0
#[1] 0.10817

mean(b$t)
#[1] 0.134634

boot.ci(b)

For more information on the results of functions boot and boot.ci see their respective help pages.

EDIT.

If you want to return several values from the boot statistic function bootCorTest, you should return a vector. In the following case it returns a named vector with the values required.

Note that I set the RNG seed, to make the results reproducible. I should already have done it above.

set.seed(7612)    # Make the results reproducible

bootCorTest2 <- function(data, i){
    d <- data[i, ]
    res <- cor.test(d$x, d$y)
    c(stat = res$statistic, p.value = res$p.value)
}


b2 <- boot(dat, bootCorTest, R = 1000)

b2$t0
#  stat.t  p.value 
#1.841083 0.108173


colMeans(b2$t)
#[1] 2.869479 0.133857