# Interpretation of the p-values

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Tiago Dias on 13 Jun 2018
Commented: Tiago Dias on 21 Jun 2018
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

Jeff Miller on 20 Jun 2018
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 on 21 Jun 2018
(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.