corrcoef - p-value calculation

Hi, I have read the description. "The p-value is computed by transforming the correlation to create a t statistic having n-2 degrees of freedom, where n is the number of rows of X."

But is this the same as saying significance of correlation was determined using t-test?

Thanks, S

Answer 1

[John D'Errico]

Is it the same as ... ? A t statistic was used in that computation. But that does not imply equivalence.

For example, I (together with a friend) built a table recently in my shop. As part of that effort, we used a saw, a chisel, a rasp, sandpaper, screwdriver, drill, router, as well as MANY other tools. Would it be correct to say that the table was built using a saw? The latter statement implies that only a saw was used. In fact, many other tools were necessary.

Similarly, when you choose to state that a t-test was used to determine significance, you leave out information that was crucial. In fact, a specific transformation was necessary, and without that transformation, a t-test would be meaningless. That t-test was not applied directly to a correlation coefficient, but to a transformation thereof.

There are limits of course. Is it necessary to state that algebra or even arithmetic was employed? I think not.

Answer 2

[sas0701]

Hi, I understand. this is for a paper. I want to describe in one sentence how the significance was calculated for the correlation values. I.e. I use the p value <0.05. But I need to decribe it.

What do you suggest?

[Peter Perkins]

The p-values from corrcoef use a statistic that is (approximately) t-distributed, but this almost completely unrelated to the t-test that you're thinking of. The latter is a test for the null hypothesis

H0: two variables are from distributions that have the same mean (and equal variance)

whwereas the p-values from corrcoef are for the null hypothesis

H0: two variables are uncorrelated.

I'm sure Wikipedia has a description, and the doc for corrceof does actually say it:

"... a matrix of p-values for testing the hypothesis of no correlation. Each p-value is the probability of getting a correlation as large as the observed value by random chance, when the true correlation is zero."