# RE: [R] Interpreting Results of Bootstrapping

From: Liaw, Andy <andy_liaw_at_merck.com>
Date: Sun 11 Jul 2004 - 11:36:14 EST

Have you actually look at plot(x1, x2)? That ought to be quite enlightening.

You have one data point:

x1 x2
25.240 6.744

that's way out in the upper right. Every bootstrap sample that include that point will give an correlation that's high, and every bootstrap sample that does not include that point will give low (near zero) correlation. Now, the probability that one point is included in a bootstrap sample is roughly 63.8%. You can easily see that:

> mean(b\$t>.5)

[1] 0.6385

Andy

> From: Y C Tao
>
> I tried to bootstrap the correlation between two
> variables x1 and x2. The resulting distribution has
> two distinct peaks, how should I interprete it?
>
> The original code is attached.
>
> Y. C. Tao
>
> ----------------
>
> library(boot);
>
> my.correl<-function(d, i) cor(d[i,1], d[i,2])
>
> x1<-c(-2.612,-0.7859,-0.5229,-1.246,1.647,1.647,0.1811,-0.0709

```7,0.8711,0.4323,0.1721,2.143,
```

> 4.33,0.5002,0.4015,-0.5225,2.538,0.07959,-0.6645,4.521,-1.371,
> 0.3327,25.24,-0.5417,2.094,0.6064,-0.4476,-0.5891,-0.08879,-0.
> 9487,-2.459e-05,-0.03887,0.2116,-0.0625,1.555,0.2069,-0.2142,-
> 0.807,-0.6499,2.384,-0.02063,1.179,-0.0003586,-1.408,0.6928,0.
689,0.1854,0.4351,0.5663,0.07171,-0.07004);
>
> x2<-c(0.08742,0.2555,-0.00337,0.03995,-1.208,-1.208,-0.001374,
> -1.282,1.341,-0.9069,-0.2011,1.557,0.4517,-0.4376,0.4747,0.049
> 65,-0.1668,-0.6811,-0.7011,-1.457,0.04652,-1.117,6.744,-1.332,
> 0.1327,-0.1479,-2.303,0.1235,0.5916,0.05018,-0.7811,0.5869,-0.
> 02608,0.9594,-0.1392,0.4089,0.1468,-1.507,-0.6882,-0.1781,0.54
> 34,-0.4957,0.02557,-1.406,-0.5053,-0.7345,-1.314,0.3178,-0.210
> 8,0.4186,-0.03347);
>
> b<-boot(cbind(x1, x2), my.correl, 2000)
> hist(b\$t, breaks=50)
>

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