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

1. Mar 29, 2015

### 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.

2. Mar 29, 2015

### Staff: Mentor

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.

3. Mar 29, 2015

### fluidistic

From the program itself:
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?

4. Mar 29, 2015

### 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

5. Mar 29, 2015

### fluidistic

Thank you very much guys!