point-biserial correlation
John,
Thanks for sharing the code to the R community. I am new to biserial
correlation, and had just tried your code for the following data:
cor.biserial(as.factor(c(0,1,0,0,0,1,1,0,1,1,1)), c(1.2, 4.5, 0.97, 1.02, 1.4,3.8,3.97,1.23,3.78,4.23,4.76))
$rbis:
0
-1.233783
$rhobis:
0
0.378785
$z:
0
-3.257211
$alpha:
0
0.0005625642
$N:
[1] 11
Is it possible to have a biserial correlation greater than 1 or less than
-1? I undrestand that normal correlation like Pearson should be between -1
and 1. And if biserial correlation can be beyond the boundary, then how big
can be seen as a good correlation? Since if we use Pearson correlation,
people can usually claim above 0.8 will be a good correlation though it's
arbitrary.
The biserial correlation includes a correction that assumes that the dichotomous variable is a discretization of some latent normally distributed variable. Of course, any departure from this assumption may result in meaningless correction and values outside [-1;1] may be observed. As to what a "good" correlation is, you should not judge of it by reference to some a priori fixed value, as it depends upon sample size. Look at the p-value. Yvonnick Noel, PhD. U. of Lille 3 FRANCE