> It might be dismissably more likely than 0%, so little more that you might conclude it is basically 0%, but it still is >0% in the mathematical sense. Therefo

> It might be dismissably more likely than 0%, so little more that you might conclude it is basically 0%, but it still is >0% in the mathematical sense. Therefore seeing correlation should imply correlation. I don't agree in the general case. A counter-example is that a purely random data set will have correlations, which by definition imply absolutely nothing about anything other than the random data set. This is addressed in the last sentence of the OP: > That is, correlation in the data you happen to have (even if it happens to be “statistically significant”) does not necessarily imply correlation in the population of interest.