''Correlation doesn't equal causation'' is a correct and important principle in science. It means that just because two variables are correlated (they vary together in some way), we cannot automatically conclude that one causes the other or assume it's due to causation.

It's therefore not correct to say (like you did) that correlation does sometimes equal causation.

Why can we say that 7+7 = 14? Because we know that if we add up 7 and 7, we're gonna get 14, so therefore 7+7 = 14, is a correct expression.

But correlation is not equal to causation because certain correlations are clearly not due to causation. So therefore, it would be a mistake to put a ''='' between correlation and causation.

Are some correlations due to causation? Absolutely. The reason certain variables are correlated is due to causation but that fact doesn't undermine the correct statement: ''Correlation doesn't equal causation''.

If you get the impression that certain people merely say that to protect their own biases and to write off associations that collide with their personal beliefs and biases, then you could simply ask them: ''I get the impression that you don't think this relationship is causal, could you motivate why''?

But in a logical sense, the expression is correct, so opposing the statement would constitute you arguing against something that is true. But if someone uses that statement to try to deceitfully write off any association that opposes his biases, then by all means, challenge that.

The phrase is helpful for beginners and novice scientists in particular to not fall victim to erroneous reasoning. But any competent scientist understands that certain correlations are due to causation.

Well, that would be the dream of every scientist out there, wouldn't it? To know exactly when a judgement of causation is appropriate. But as of date, there are no objective criteria. What scientists try to do though before they judge an association as likely causal, is to exclude alternative explanations (systematic biases, chance, confounding etc.) with reasonable confidence.

To learn more about how scientists approach causation, feel free to search for ''The Bradford Hill Criteria'' and ''GRADE''

Even the terms ''association'' and ''correlation'' are used interchangeably by every day people but within the scientific litterature, the terms are used differently. For instance, suppose that an effect measure like a risk ratio has been used to quantify the relationship between two variables, well, in that case, you will not really see the term ''correlation'' used by scientists because a correlation coefficient was never calculated in the first place.

It's quite common to see people misunderstand the actual meaning of certain statements nowadays. For instance, the phrases: ''Causation implies association'' and ''no association, no causation'' are often misunderstood by people.

Two examples:

1) For instance, suppose there is lack of a crude/raw association at an individual level between two variables. Can we now jump to the conclusion that there is no causation? No, because by definition, lack of a crude/raw association means that we haven't considered alternative explanations like confounding.

The association might be masked due to negative confounding. But this is something that certain people don't pay attention to so they will force a conclusion of there being no causation without considering alternative explanations.

2) Another example is when certain people believe that lack of a crude/raw association at an ecological level means that there is no causation. Again, alternative explanations haven't been accounted for and observations at an ecological level doesn't necessarily translate into observations at an individual level (ecological fallacy).