However, in casual use, the word "implies" loosely means suggests rather than requires. The idea that correlation and causation are connected is certainly true; where there is causation, there is a likely correlation. Indeed, correlation is used when inferring causation; the important point is that such inferences are made after correlations are confirmed as real and all causational relationship are systematically explored using large enough data sets.

Answer this question: when does correlation allow you to infer causation? Let's give stream of consciousness first:
This is the relevant information: Indeed, correlation is used when inferring causation; the important point is that such inferences are made after correlations are confirmed as real and all causational relationship are systematically explored using large enough data sets.
So, the final answer is after correlations are confirmed as real and all causational relationship are systematically explored using large enough data sets.