Naive question on p value...

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spasmous...

Posted: Fri Jul 18, 2008 1:56 pm

Guest

I just found out that correlation coefficient is the square root of
the r-squared. I understand the latter but never quite know what the
former was. Another statistics term "p value" also is pretty murky to
me - I'm guessing for the same reason correlation coefficient was
murky, i.e. lots of hoopla and wordy explanation of it. I'm wondering
if there a technical definition of it (or <gasp> a formula I can look
at)?

I know it's the probability of obtaining the observed correlation
under the null hypothesis (or something like that Wink

but I'd like to
know the actual equation. Can anyone advise? Thanks.

Jack Tomsky...

Posted: Fri Jul 18, 2008 3:20 pm

Guest

Quote:

I just found out that correlation coefficient is the
square root of
the r-squared. I understand the latter but never
quite know what the
former was. Another statistics term "p value" also is
pretty murky to
me - I'm guessing for the same reason correlation
coefficient was
murky, i.e. lots of hoopla and wordy explanation of
it. I'm wondering
if there a technical definition of it (or <gasp> a
formula I can look
at)?

I know it's the probability of obtaining the observed
correlation
under the null hypothesis (or something like that Wink

but I'd like to
know the actual equation. Can anyone advise? Thanks.

You're pretty close. For a simple correlation r between y and x, under the null hypothesis that the population correlation rho is zero,

t = sqrt(N-2)*r/sqrt(1-r^2)

has a t distribution with N-2 degrees of freedom. The p-value is double the probability that t(N-2) exceeds sqrt(N-2)*|r|/sqrt(1-r^2).

For a multiple correlation R between y and (x1, ..., xp), under the null hypothesis that the population multiple correlation is zero,

F = (N-p-1)*R^2/[p*(1-R^2)]

has an F distribution with p and N-p-1 degrees of freedom.

The p-value is the probability that F(p,N-p-1) exceeds (N-p-1)*R^2/[p*(1-R^2)].

Jack

Paul Rubin...

Posted: Fri Jul 18, 2008 8:28 pm

Guest

spasmous wrote:

Quote:

I just found out that correlation coefficient is the square root of
the r-squared.

For a simple regression. For a multiple regression, the coefficient of
multiple determination (a.k.a. R-squared) is the square of the
correlation between the predicted values of the dependent variable and
the actual values.

Quote:

I understand the latter but never quite know what the
former was. Another statistics term "p value" also is pretty murky to
me - I'm guessing for the same reason correlation coefficient was
murky, i.e. lots of hoopla and wordy explanation of it. I'm wondering
if there a technical definition of it (or <gasp> a formula I can look
at)?

I know it's the probability of obtaining the observed correlation
under the null hypothesis (or something like that Wink

but I'd like to
know the actual equation. Can anyone advise? Thanks.

The p-value of a correlation coefficient is the (approximate) type I
risk in testing the null hypothesis of a true correlation of zero v. the
two-sided alternative that the true correlation is something other than
zero. So it's essentially the probability of getting an estimated
correlation coefficient as large as _or larger than_ the one you got _in
magnitude_ if in fact the true correlation is zero. The test is usually
based on Fisher's z-transformation, so for a formula you could look at
http://en.wikipedia.org/wiki/Fisher_transformation.

/Paul

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