You are right, the outlier caused the problem. Using Spearman or Kendall's correlation seems to solve the problem. Thanks!
Y. C. Tao --- [EMAIL PROTECTED] wrote: > Hi! > > Simply plot(x1,x2): you will see that there is one > point > (number 23) at (x1,x2) = (25.34,6.744) which is a > very > long way from all the other points (which, among > themselves, > form a somewhat diffuse cluster with some suggestion > of > further structure). > > When you bootstrap, the correlation you obtain in > any sample > will depend on whether or not this outlying point is > included > in the sample. If it is included, this single point > will generate > a relatively high value of the correlation > coefficient simply > because it is such a long way from all the others > (i.e. it is > highly influential). > > If it is not included, then the diffuse character of > the other > points will generate a very low value of the > correlation > coefficient. > > > cor(x1,x2) > [1] 0.7471931 > > cor(x1[-23],x2[-23]) > [1] 0.03914653 > > Therefore your bootstrap distribution will have two > peaks: one > peak, around 0.75, corresponding to the bootstrap > samples which > include this outlying point, and the other, around > 0, corresponding > to the bootstrap samples which do not include it. > > This is the explanation and, at the same time, the > interpretation. > > Best wishes, > Ted. > > On 11-Jul-04 Y C Tao wrote: > > 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, > > > -0.07097,0.8711,0.4323,0.1721,2.143,4.33,0.5002, > > > 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, > > > 0.4747,0.04965,-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,-0.1781,0.5434,-0.4957, > > > 0.02557,-1.406,-0.5053,-0.7345,-1.314,0.3178,-0.2108, > > 0.4186,-0.03347); > > > > b<-boot(cbind(x1, x2), my.correl, 2000) > > hist(b$t, breaks=50) > > [The above rearranged to have 7 values in each > conplete line] > > > > -------------------------------------------------------------------- > E-Mail: (Ted Harding) <[EMAIL PROTECTED]> > Fax-to-email: +44 (0)870 167 1972 > Date: 11-Jul-04 > Time: 10:40:34 > ------------------------------ XFMail > ------------------------------ > ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
