R help - Apr 2004 - confidential interval of correlation coefficient using bootstrap

I tried 2 methods to estimate C.I. of correlation coefficient of variables x and
y:
> 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)
#METHOD 1: Pearson's
**********************************************************
> cor.test(x, y, method = "pearson", conf.level = 0.95)
        Pearson's product-moment correlation

data:  x and y 
t = 1.8411, df = 7, p-value = 0.1082
alternative hypothesis: true correlation is not equal to 0 
95 percent confidence interval:
 -0.1497426  0.8955795 
sample estimates:
      cor 
0.5711816 
***********************************************************

#METHOD 2: bootstrap
***********************************************************
> boot(cbind(x,y), cor, 200)
ORDINARY NONPARAMETRIC BOOTSTRAP


Call:
boot(data = cbind(x, y), statistic = cor, R = 200)


Bootstrap Statistics :
     original     bias    std. error
t1* 0.5429120 -0.5232893   0.3799117
t2* 0.3832856 -0.3779026   0.3876666
************************************************************

'cor.test' gave the value of cor as 0.5711816.  Why did 'boot'
give two original cors: t1 and t2.  And why does none of t1 and t2 equal to what
'cor.test' gave.

Thank you very much

Xiao

You are not using boot() correctly.  Please do try reading the help page, 
which says

statistic: ...

  In all other cases 'statistic' must take at least two arguments.  The
  first argument passed will always be the original data. The second will
  be a vector of indices ...

so you need a function of two args like
> f <- function(data, i) cor(data[i, 1], data[i, 2])
> boot(cbind(x,y), f, 200)
ORDINARY NONPARAMETRIC BOOTSTRAP


Call:
boot(data = cbind(x, y), statistic = f, R = 200)


Bootstrap Statistics :
     original     bias    std. error
t1* 0.5711816 0.05765583   0.2178101


However, once you have done that you need a way to get a confidence 
interval, and you will find ?abc.ci has an example for you, using 
correlations.


On Sat, 10 Apr 2004, XIAO LIU wrote:
> I tried 2 methods to estimate C.I. of correlation coefficient of variables
x and y:
> 
> > 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)
> 
> #METHOD 1: Pearson's
> **********************************************************
> > cor.test(x, y, method = "pearson", conf.level = 0.95)
> 
>         Pearson's product-moment correlation
> 
> data:  x and y 
> t = 1.8411, df = 7, p-value = 0.1082
> alternative hypothesis: true correlation is not equal to 0 
> 95 percent confidence interval:
>  -0.1497426  0.8955795 
> sample estimates:
>       cor 
> 0.5711816 
> ***********************************************************
> 
> #METHOD 2: bootstrap
> ***********************************************************
> > boot(cbind(x,y), cor, 200)
> 
> ORDINARY NONPARAMETRIC BOOTSTRAP
> 
> 
> Call:
> boot(data = cbind(x, y), statistic = cor, R = 200)
> 
> 
> Bootstrap Statistics :
>      original     bias    std. error
> t1* 0.5429120 -0.5232893   0.3799117
> t2* 0.3832856 -0.3779026   0.3876666
> ************************************************************
> 
> 'cor.test' gave the value of cor as 0.5711816.  Why did
'boot' give two original cors: t1 and t2.  And why does none of t1 and
t2 equal to what 'cor.test' gave.
> 
> Thank you very much
> 
> Xiao
-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
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