point-biserial correlation

On 31 Mar 2003 at 15:07, Noel Yvonnick wrote:

[...]

Note that the point-biserial correlation is nothing but the standard
correlation coefficient when one of the variables is dichotomous, so
that cor(.) is OK.

Yes, this is a misleading subject.

The biserial is different and includes a correction for the so-called
"point of dichotomy". The following should work (translating a formula
found in a psychometric manual) :

[...]

  # Biserial correlation
  # Be cautious in interpreting the sign :
  # depends upon the ordering of levels(x)
  ((m[1]-m[2])/Sy)*(f[1]*f[2]/dnorm(f[1]-.5))

Thanks a lot for your help. Your code inspired me to do some modifications.

(1) Following a German statistic book (Bortz, J?rgen, 1993: Statistik.
Heidelberg: Springer) I use the following term "dnorm(qnorm(f[1]))" instead
of "dnorm(f[1]-.5)".

(2) I added some code for handling NA's.

(3) Finaly, it is now possible to do some significance test for rbis.


Bernd


# Modification of Noel Yvonnick function for computing biserial
correlations # x.na: 0/1 variable
# y.na: continuous variable
cor.biserial = function(x.na,y.na)
{
  x <- x[!is.na(y.na) & !is.na(x.na)]
  y <- y[!is.na(y.na) & !is.na(x.na)]

  stopifnot(is.factor(x))
  stopifnot(length(levels(x))==2)
  stopifnot(length(x)==length(y))

  N = length(y)

  # Success / Failure frequencies
  n <- table(x)
  f = table(x)/length(x)

  # Means of success/failure groups on the global score
  m = tapply(y,x,mean)

  # Variance of the global score
  Sy = sqrt(var(y)*(N-1)/N)

  # Biserial correlation
  # Be cautious in interpreting the sign :
  # depends upon the ordering of levels(x)
  rbis <- ((m[1]-m[2])/Sy)*(f[1]*f[2]/dnorm(qnorm(f[1])))

  # significance test for rbis
  rhobis <- sqrt(n[1]*n[2])/(dnorm(qnorm(f[1]))*N*sqrt(N))
  z <- rbis/rhobis
  alpha <- ifelse(z<0,pnorm(z),1-pnorm(z))

  return(rbis,rhobis,z,alpha,N)
}