# [R] bootstrapped correlation confint lower than -1 ?

Liviu Andronic landronimirc at gmail.com
Sun Aug 16 12:22:29 CEST 2009

```Dear R users,
Does the results below make any sense? Can the the interval of the
correlation coefficient be between  *-1.0185* and -0.8265 at 95%
confidence level?
Liviu

> library(boot)
> data(mtcars)
> with(mtcars, cor.test(mpg, wt, met="spearman"))

Spearman's rank correlation rho

data:  mpg and wt
S = 10292, p-value = 1.488e-11
alternative hypothesis: true rho is not equal to 0
sample estimates:
rho
-0.88642

Warning message:
In cor.test.default(mpg, wt, met = "spearman") :
Cannot compute exact p-values with ties
> corr.fun <- function(data, indices) {
+ data.samp <- data[indices,] # allows boot to select sample
+ tmp.corr <- with(data.samp, cor.test(mpg, wt, met="spearman"))
+ return(tmp.corr\$estimate)
+ }
> corr.boot <- boot(mtcars, corr.fun, R=1000)
There were 50 or more warnings (use warnings() to see the first 50)
> corr.boot

ORDINARY NONPARAMETRIC BOOTSTRAP

Call:
boot(data = mtcars, statistic = corr.fun, R = 1000)

Bootstrap Statistics :
original   bias    std. error
t1* -0.88642 0.012992    0.050042
> boot.ci(corr.boot, type="basic")
BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
Based on 1000 bootstrap replicates

CALL :
boot.ci(boot.out = corr.boot, type = "basic")

Intervals :
Level      Basic
95%   (-1.0185, -0.8265 )
Calculations and Intervals on Original Scale

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```