Ivo

The list of what it does not mean is the practical half. In particular it says nothing about the size of the effect, and with a large enough sample a difference far too small to care about clears the bar comfortably.

Which is why a significant result on its own does not tell you whether anything worth acting on happened.

Unlikely to have occurred by chance, under what assumption. That missing clause is the whole problem.

Teach this and get it wrong most years. The version that works: assume there is no real effect, then ask how often data this extreme would show up anyway. Significant means the answer is rarely, under that assumption.

The assumption is the part that goes missing in every casual explanation, and without it the sentence really is circular.