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I got correlation coefficient r = 0.33 but my p-value = 0.124 > 0.05 Is there a non-significant correlation or no correlation at all?

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I got correlation coefficient r = 0.0001 but my p-value = 0.000001 < 0.05. I have a massive dataset. Is there a non-significant correlation or no correlation at all?

I flipped a penny one and a dime once and they both landed on heads. I got correlation coefficient r = 1 but my p-value is more than 0.05.

The "technically correct" answer to your question may or may not be what you want. However, it is this:

I got correlation coefficient r = 0.33 but my p-value = 0.124 > 0.05 Is there a non-significant correlation or no correlation at all?

There is a non-significant correlation (the same as in the second example).