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

Duncan Murdoch murdoch at stats.uwo.ca
Sun Aug 16 12:50:11 CEST 2009

```Liviu Andronic wrote:
> 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?
>

Why not?  You used an ordinary nonparametric bootstrap, so it doesn't
know that the parameter is constrained.  The bootstrapped estimates of
the correlation will all lie between -1 and 1, but the basic bootstrap
confidence interval is not just the central 95% of the bootstrap
estimates (that's the percentile confidence interval), the basic
interval is twice the original estimate minus that range.  See the
Davison and Hinkley reference.

Duncan Murdoch
> 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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>
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>

```