MATLAB: Corrcoef – p-value calculation

Question

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

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.