0.7 correlation but almost 0 p-value, how to interpret?

[fluidistic]

Hi guys,
I've compared 2 samples of data from which I expected some correlation. The result is that the correlation is about 0.7 while the p-value (calculated by a software) is about $10^{-92}$.
I don't really know how to interpret this low p-value. Does that mean that I can fully trust that the correlation is indeed 0.7 or does that mean that not at all. That it's extremely unlikely.
Or does that implies something else?
Thank you.

 

[mfb]

The p-value for what?

For being uncorrelated? Then you know it is correlated for sure, and probably with a correlation close to 0.7. Apart from very weird cases, this value of 0.7 should be quite precise, otherwise I don't see how you would get such a small p-value.

 

[fluidistic]

The p-value for what?

For being uncorrelated? Then you know it is correlated for sure, and probably with a correlation close to 0.7. Apart from very weird cases, this value of 0.7 should be quite precise, otherwise I don't see how you would get such a small p-value.

From the program itself:

ThePearson correlation coefficient measures the linear relationship
between two datasets.Strictly speaking,Pearson's correlation requires
that each dataset be normally distributed. Like other correlation
coefficients, this one varies between -1 and +1 with 0 implying no
correlation. Correlations of -1 or +1 imply an exact linear
relationship. Positive correlations imply that as x increases, so does
y. Negative correlations imply that as x increases, y decreases.

The p-value roughly indicates the probability of an uncorrelated system
producing datasets that have a Pearson correlation at least as extreme
as the one computed from these datasets. The p-values are not entirely
reliable but are probably reasonable for datasets larger than 500 or so.

So... the probability that an uncorrelated data set having a correlation of 0.70 or more is basically 0, is what the p-value is telling me?
But "uncorrelated" from which data set? From both that I tested?

 

[FactChecker]

It means that your two data sets are very unlikely to be uncorrelated with each other, assuming that you have enough data . It would be a very freak occurrence for two uncorrelated data sets to appear that well correlated just by luck

 

[fluidistic]

Thank you very much guys!