Talk:Point-biserial correlation coefficient
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This is wrong. The point biserial correlation coefficient is still important today in the field of Psychometrics. —The preceding unsigned comment was added by 128.97.86.17 (talk • contribs) 08:57, 21 June 2006 (UTC)
I would like to suggest to delete the "external information" link, since the formula for r_pb on that page is wrong. That is, it makes exactly the mistake I am warning about. Kmir78 01:50, 18 January 2007 (UTC)
Do you have a source with the correct formula? MrArt 05:43, 18 January 2007 (UTC)
Glass and Hopkins (Statistical Methods in Education and Psychology (3rd Edition)) have the correct formula, but I could also easily put a derivation from the normal formula in here. I don't know any online source. Kmir78 04:48, 19 January 2007 (UTC)
[edit] Wrong formula?
It is not easy to just say that a formula is wrong if one doesn't know its meaning. Oe should at least distinguish between population and sample. In the population the coefficient is a parameter and in the sample an estimator of this parameter.
Parameter:
with
- μx = E(Y | X = x)
and
- p = P(X = 1)
Estimator
where M1,M0 are the sample means of Y for X=1 and X=0 and N1 the number of Y's with X=1 and SY is the usual sample standard deviation "with n-1 in the denominator".
If one takes for SY the sample standard deviation "with n the denominator". ", the formula reads:
Even in the case where SY is the usual sample standard deviation "with n-1 in the denominator" the formula:
gives a good estimator of ρ.Nijdam 14:07, 24 January 2007 (UTC)
Asymptotically, both formulas will yield the same result. But as far as I know, rpb is supposed to equal rXY in the sample. rXY is independent of the denominator n or n − 1 and therefore, rpb with 'some n' stuck in there somewhere instead of n − 1 will not equal rXY. Kmir78 06:40, 28 January 2007 (UTC)
