corrcoef - p-value calculation
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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
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John D'Errico
on 9 Feb 2015
Edited: John D'Errico
on 9 Feb 2015
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.
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sas0701
on 10 Feb 2015
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Peter Perkins
on 10 Feb 2015
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."
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