Interpretation of the p-values

Hello,

So I used the corr function on my matrix A that is 5x4,

A =
    0.1576    0.1419    0.6557    0.7577
    0.9706    0.4218    0.0357    0.7431
    0.9572    0.5784    0.8491    0.7458
    0.4854    0.7542    0.9340    0.6547
    0.8003    0.9595    0.6787    0.1712

[r p] = corr(A,'rows','pairwise')

I know already the difference of 'complete' and 'pairwise', what I understood is that is relevant if I got NaN in some observations.

r =
    1.0000    0.4448   -0.3635   -0.1775
    0.4448    1.0000    0.3492   -0.7784
   -0.3635    0.3492    1.0000   -0.1507
   -0.1775   -0.7784   -0.1507    1.0000

p =
    1.0000    0.4530    0.5475    0.7752
    0.4530    1.0000    0.5646    0.1210
    0.5475    0.5646    1.0000    0.8089
    0.7752    0.1210    0.8089    1.0000

What I would like to question is about the values of p-values. For example p(2,4) = p(4,2) = 0.1210 and is > 0,05 (the value of alpha), but what this mean about the value of R(2,4) = -0.7784, is this a good thing, is the correlation good or should i ignore this correlation? What i read is that p<0.05 is a good thing, but what if p=0.47 > 0.05 and the R is 0.995 is a bad correlation?

Hope you understand what my doubt is.

Thanks

Answer 1

[Jeff Miller]

I am not sure I understand your question, but maybe this will help:

p is the probability of getting such an extreme correlation (as extreme as the one in your data) by chance when the true population correlation is 0. So, p depends on the observed correlation, and it also depends on the sample size. If the r is 0.995, p cannot be 0.47.

[Tiago Dias]

Ok, it was an example, but I choose a bad one it seems.

So for the example I gave, I don't have any p-value < 0.05, so I must reject all my values of r? What I understood is that p<0.05 is good, but what happen when p >0.05, I must reject the value of r?

[Jeff Miller]

p values are pretty complicated, but Google will help you find many sources trying to explain them. I can’t really answer your question because I don’t know what you mean by "I must reject all my values of r". In my view, r is a summary statistic describing the results in a sample, just like a sample mean, so it is an observed fact—not something to be accepted or rejected.

In practical terms, when testing for correlation, a value of p>.05 essentially means “The observed data in this sample do not provide strong evidence that the true correlation (i.e., for the whole population) differs from zero.” So, all you can conclude is that the true populations correlations could all be zero, despite the many nonzero correlations that you obtained in your sample data.

[Tiago Dias]

(a value of p>.05 essentially means “The observed data in this sample do not provide strong evidence that the true correlation (i.e., for the whole population) differs from zero.” )

ok thanks, and when is <.05, it must provide strong evidence that the true correlation differs from zero. Will try to find some paper with a better explanation about this topic.

My understanding was that p-value was a validation criteria for the correlation values.