This is perfectly good common-sense reasoning that explains why the correlation is undefined. If your audience has any notion whatsoever of what correlation means, they will understand this. If not, trying to phrase the same argument in terms of math will not help; it will just make it impossible for your audience to engage with your argument.
If the audience is mathematically sophisticated, then writing out the formula for Pearson’s correlation coefficient is just going to distract them from the real issue, which is that the saying should refer to statistical dependence, rather than correlation. In other words, C’s argument only addresses the literal meaning of B’s words, not the substance behind them.
I acknowledge that using the wrong terminology to the wrong audience will make their eyes glaze over and be counter-productive.
If your audience has any notion whatsoever of what correlation means, they will understand this.
I disagree about that. Until I actually took a course in statistics, I wouldn’t have been sure whether the correlation was undefined or just misleading in that case. Again, I agree that not everyone needs this level of precision.
the real issue, which is that the saying should refer to statistical dependence, rather than correlation.
An important issue, but a completely different one. If B said “that is statistical dependence, not causation”, wouldn’t they be equally wrong in exactly the same way?
If B said “that is statistical dependence, not causation”, wouldn’t they be equally wrong in exactly the same way?
B would be wrong in the exact same way. So the true reason that B is wrong needs to apply in both cases. On the other hand, appealing to the correlation formula only defeats the correlation version of the argument.
This is perfectly good common-sense reasoning that explains why the correlation is undefined. If your audience has any notion whatsoever of what correlation means, they will understand this. If not, trying to phrase the same argument in terms of math will not help; it will just make it impossible for your audience to engage with your argument.
If the audience is mathematically sophisticated, then writing out the formula for Pearson’s correlation coefficient is just going to distract them from the real issue, which is that the saying should refer to statistical dependence, rather than correlation. In other words, C’s argument only addresses the literal meaning of B’s words, not the substance behind them.
I acknowledge that using the wrong terminology to the wrong audience will make their eyes glaze over and be counter-productive.
I disagree about that. Until I actually took a course in statistics, I wouldn’t have been sure whether the correlation was undefined or just misleading in that case. Again, I agree that not everyone needs this level of precision.
An important issue, but a completely different one. If B said “that is statistical dependence, not causation”, wouldn’t they be equally wrong in exactly the same way?
B would be wrong in the exact same way. So the true reason that B is wrong needs to apply in both cases. On the other hand, appealing to the correlation formula only defeats the correlation version of the argument.
Ah, I see what you mean. You’re right.