[R] Re: point-biserial correlation

[Noel Yvonnick]

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