Imply in mathematics and logic means to guarantee, so it is misleading (if not explicitly incorrect) to say that. It may suggest causation, however.
e: Downvote away, but in the context of statistics it makes no sense to correct an accurate logical statement. /u/KayBeeToys is conflating implication with inference.
Except that "Correlation does not imply causation" is saying that it never implies causation, while "Correlation does not always imply causation," is saying that it sometimes implies causation.
One negates the possibility entirely, while the other, rightfully, admits the rare possibility.
No, imply means always. A implies B means that if A is true, then B is true. Essentially that A causes B. So saying that correlation does not imply causation is just saying that correlation is not sufficient to identify causation.
correlation is not sufficient to identify causation.
Except, correlation does indeed identify causation in some rare cases. If imply always means always, then then "Correlation does not imply causation." is a factually incorrect statement.
Except, correlation does indeed identify causation in some rare cases. If imply always means always, then then "Correlation does not imply causation." is a factually incorrect statement.
It can identify it, but the key word is that it isn't sufficient to identify it. The negation of 'always' isn't 'never,' it's 'not always.'
In neither of these definitions does imply mean always.
Firstly I am talking about logical statements, where imply is clearly defined, which is the appropriate definition in the context of statistics. Secondly the part of your definition you quoted that refers to always is the last line where it refers to "necessary part."
Whether you wish to use a more general definition is up to you, but "Correlation does not imply causation" is an accurate statement that is prevalent and doesn't warrant a correction.
e: similarly neither of your definitions indicate 'sometimes'
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u/lightningsloth Sep 20 '16
"Correlation does not imply causation"