Message-ID: <200304041142.29146.noel@univ-lille3.fr>
Date: 2003-04-04T11:42:29Z
From: Yvonnick Noel
Subject: point-biserial correlation
In-Reply-To: <20030403233703.79803.qmail@web41206.mail.yahoo.com>
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