I’m using ‘imply’ in an empirical rather than logical sense
I feel like this is using the word somewhat differently than is meant by the phrase you are discussing. I’ve always interpreted “correlation doesn’t imply causation” to mean that if X and Y are correlated you can’t necessarily say that X → Y or Y → X (probably based on some prior about the direction like timing), not that correlation is somehow completely unrelated to causation.
Congrats on always interpreting the phrase that way! Of the folks I’ve discussed this with in person, every one of them had the interpretation that things can be correlated without either one causing the other or a common cause.
I would be surprised if “correlation does’t imply causation” would have become so popular if most people interpreted it as strictly expanding the options from X → Y or Y → X to include common cause (and now might ask a stats-professor friend to run a poll to see which of these interpretations most people hold in their intro stats class), but I think your interpretation is correct. I certainly don’t want to attack a strawman version of the phrase, but if >30% of people interpret it that way I’ll conclude it’s not a strawman.
I feel like this is using the word somewhat differently than is meant by the phrase you are discussing. I’ve always interpreted “correlation doesn’t imply causation” to mean that if X and Y are correlated you can’t necessarily say that X → Y or Y → X (probably based on some prior about the direction like timing), not that correlation is somehow completely unrelated to causation.
Congrats on always interpreting the phrase that way! Of the folks I’ve discussed this with in person, every one of them had the interpretation that things can be correlated without either one causing the other or a common cause.
I would be surprised if “correlation does’t imply causation” would have become so popular if most people interpreted it as strictly expanding the options from X → Y or Y → X to include common cause (and now might ask a stats-professor friend to run a poll to see which of these interpretations most people hold in their intro stats class), but I think your interpretation is correct. I certainly don’t want to attack a strawman version of the phrase, but if >30% of people interpret it that way I’ll conclude it’s not a strawman.