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Homework answers / question archive / Post-hoc fallacy is that condition where regression shows a high degree of correlation (R square is high), but there is no real cause-effect relationship between the independent and dependent variables
Post-hoc fallacy is that condition where regression shows a high degree of correlation (R square is high), but there is no real cause-effect relationship between the independent and dependent variables. For example, when the rooster crows each morning, the sun pops up every time (even if we can't see it). R square would be 1.00 in this case, but does that mean the rooster's crow actually caused the sun to rise? Clearly not, that would be post-hoc fallacy to conclude otherwise...there is no real cause and effect.
After doing a regression analysis on two sets of data, how would you go about ensuring that you have not fallen into the post-hoc fallacy trap?
How would you explain post-hoc fallacy to your boss or CO, who has no statistical background?
In terms of explaining this to someone with no statistical background, the example in the first paragraph does a good job of this. Can you think of other instances in which there is a strong correlation (positive or negative) but no causation? For instance, ice cream sales and snow shovel sales are very strongly (negatively) correlated, but they do not cause each other. Rather, both are influenced by the weather. When two events are both caused by a third event, they will be correlated, but will not have a causal relationship.
If you do a regression analysis and find that the data are correlated, as long as you say that you have found a strong correlation, and don't claim that one variable causes the other, you will be safe from falling into the post-hoc fallacy trap. If you can think of a good hypothesis for a causal relationship, you can propose that theory, but then you have to find more evidence to support that hypothesis.
For instance, if you think A causes B, first you should show that A and B are correlated. Then, if that is the case, you should show that (1) whenever A happens, B also happens and (2) that B never happens unless A also happens.
