anscombe.extended {multivariance}

Extended Anscombe's Quartett

Description

The dataset extends 'anscombe' provided in the standard R-package 'datasets'. All examples feature the same correlation of 0.82, but different types of dependencies. The main aim was to extend the classical examples, which have sample size 11, to larger sample sizes. This illustrates that the implied problems of Pearson's correlation are not small sample problems! Distance multicorrelation (which coincides in this case with distance correlation) yields different values for the datasets.

Usage

anscombe.extended

Format

list with elements:

• anscombe.extended$N11 matrix with 11 samples for 5 examples the first 4 are the classical Anscombe Quartett, the fifth is a monoton relation which also features the same correlation.

• anscombe.extended$N100 same as above but 100 samples

• anscombe.extended$N1000 same as above but 1000 samples

Details

Note: Anscombe's quartett features further identical parameters besides Pearson's correlation. The extended set is only concerned with correlation.

References

This example was introduced in the reference [6] given on the main help page of this package: multivariance-package.

Examples

# Code which generates plots of all included data:
op = par(mfrow = c(3,5),mar = c(0.5,0.5,3,0.5))
for (name in c("N11","N100","N1000")) {
 for (i in 1:5) {
   x = anscombe.extended[[name]][,2*i-1]
   y = anscombe.extended[[name]][,2*i]
   plot(x,y,main = paste0("cor = ",round(cor(x,y),2),
"\n Mcor = ",round(multicorrelation(cbind(x,y),type = "pairwise",squared = FALSE),2),
"\n CMcor = ",round(copula.multicorrelation(cbind(x,y),type = "pairwise",squared = FALSE),2)),
        axes = FALSE,xlab ="",ylab = "", cex.main=1)
   # for two variables 'pairwise' coincides with
   # both values of 'total.upper.lower'.
   box()
 }
}
par(op)