P value in CORR or CORRCOEF

[Lin]

Hello!

I have a question about the CORR(or CORRCOEF) function.

In the corr document:
[RHO,PVAL] = corr(...) also returns PVAL, a matrix of p-values for testing the hypothesis of no correlation against the alternative that there is a nonzero correlation. Each element of PVAL is the p-value for the corresponding element of RHO. If PVAL(i, j) is small, say less than 0.05, then the correlation RHO(i, j) is significantly different from zero.

What happend if some p values bigger than 0.05?(eg. 0.7) Does that mean those corresponding correlations RHO are not so "reliable"? Can I use those RHO? Or I should look for some other ways?

TIA
Regards,
Lin

[arun]

You set your null hypothesis as "there is no significant difference
between x and y". if you have a 5% level of significance, alpha =
0.05, then if pVal < alpha, you reject null hypothesis and accept the
alternative hypothesis that the correlation between this particular
(i,j) is significant. Otherwise, you decide there is no correlation or
rho = 0.

hope this helps,
best, arun.

[Lin]

Thanks a lot arun.

I have one more question.

What I understood:

rho values: how "powerful" are the correlations
p values: testing the hypothesis of no correlation (null hypothesis rho=0)

For example if p > alpha, then the null hypothesis will not be rejected. One decides the corresponding rho=0 (no correlation).

One more question:

If p < alpha and the corresponding rho=0, does that mean:
1. There is no correlation
or
2. CORR/CORRCOEF is not suitable here, one should try some other functions.

[Tom Lane]

Lin, the p-value is not a goodness-of-fit measure designed to tell you if
the correlation coefficient is suitable. It's simply a measure of
significance. I would not expect to get a p-value near zero if the
corresponding correlation were also near zero.

-- Tom

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