1. Fallacies Related to Cause & Effect
There are two important fallacies, where both assume that the timing of two variables relative to each other, in and of itself, is sufficient to establish that one is the cause and the other is the effect. This assumption is wrong.

2. Post Hoc, Ergo Propter Hoc
“After this, therefore because of it.”
This is the assumption that the fact one event came after another establishes that it was caused by the other.
“After I took Zicam my cold went away fast. Therefore taking Zicam caused my cold to go away fast.”
There is an assumption that the Zicam caused the cold to go away fast.
“After I played poker my cold went away fast. Therefore playing poker caused my cold to go away fast.”
Obviously that argument is no better.

3. More Examples
“Every day the sun comes up right after the rooster crows; therefore the rooster causes the sun to come up.”
“After you drove my car it was hard to start. Therefore it was something you did that made my car hard to start.”
It is not a fallacy to think that the first event MIGHT have cause the second event. The fallacy occurs when we assume that the sequential timing of events, in and of itself, establishes cause and effect between them, as in the last example.

4. Special cases of Post Hoc
Overlooking the Possibility of Coincidence
“After Susan threw out the chain letter, she was in an automobile accident. Therefore throwing out the chain letter caused her to get in an automobile accident.”
Probably just coincidental.
Overlooking the Possibility of Common Cause
“I left the lights on when I went to bed. Next morning I woke up with a headache. Therefore leaving the lights on caused the headache.”
Common cause would be maybe you went to bed unusually tired or you were intoxicated.

5. Overlooking the Possibility of Random Variation
This fallacy occurs when we ignore the fact that values of variables fluctuate randomly.
You take two random groups of men, the average distance one group throws a football will vary randomly from the other. Just as if they were to throw the ball a second time, the average distance will vary randomly the second time as from the first.
“In our tests, we asked randomly selected men to drive a golf ball as far as they possibly could. We then had them wear our magnetic bracelet and try again. On the second occasion the men hit the ball an average of ten feet further. Our bracelet can lengthen your drive as well.”
The implication is that the bracelet caused the improvement in the average drive lengths. The improvement could be due to random variation. If the test was performed again, the drive length might decrease. The drive length is almost certain to change randomly from one trial to the next.

6. Overlooking the Possibility of Regression
This fallacy is committed when we overlook this fact: “If the average value of a variable is atypical in one measurement, it is likely to be less atypical on a subsequent measurement.”
If the average distance the randomly selected men drove a golf ball is relatively distant from the “true average” for all men, then on the second try, the average is apt to be closer to the true average. The more atypical the value is in one measurement, the more likely it is to be less atypical on the next measurement.
“ We measured the IQs of a group of students and found the average to be relatively low. Then we had them take a course on critical thinking, after which we measured their IQs again, and they were higher. Therefore the course in critical thinking raised their IQs.”

7. Since their IQ scores were apt to be higher on the second measurement anyways, the speaker has overlooked that fact and attributed the change in IQ scores to the critical thinking class, which is a fallacy.
One basketball coach talking to another coach: “The girls shot well below their average on Monday, so I made them do 50 sets of pushups. Guess what? Their average was much better on Tuesday. Pushups did the trick.”
The coach has overlooked the fact that their averages were apt to improve, even if they had been served cookies instead of having to do pushups.

8. Cum Hoc, Ergo Propter Hoc
“With this, therefore because of it.”
This fallacy occurs when we assume that two events that happen at about the same time establishes that one caused the other.
“John had a heart attack while he was saying a prayer. Therefore the prayer caused the heart attack”
If two events happen at the same time, thinking one might have been the reason for the other is not wrong, but it is never sufficient to establish that it is the reason.
“Children with long hair are better spellers than children with short hair. Therefore having long hair makes a child a better speller.”
The premise is perhaps absurd, but the conclusion does not follow in any case. Correlation does not prove causation.

9. Special case of Cum Hoc Overlooking the Possibility of Coincidence
“I got cancer when I lived under a high-voltage power line. Therefore the high-voltage power line caused my cancer.”
Possibly just coincidental.
Overlooking a Possible Common Cause
“Chimney fires and long underwear purchases increase in frequency at the very same time. Therefore chimney fires cause people to buy long underwear.
Common cause could possibly be the weather turning colder.

10. Overlooking the Possibility of Reversed Causation
“People who walk long distances enjoy good health. Therefore walking long distances will make you healthy.”
The assumption is that walking accounts for good health, but maybe it is backwards. Maybe being healthy accounts for the walking.
“Successful businesspeople often drive expensive cars. Therefore driving an expensive car will make you a successful businessperson.”
The assumption if that driving an expensive car is the cause of being successful, not the reason for it.

11. Argument by Anecdote (Casual Variety)
Just as it is a fallacy to try to support or disprove a general claim by telling a story, it is also a fallacy to try to support or disprove a cause-and-effect claim by telling a story. The latter is the Argument by Anecdote.
“I’ve heard doctors say eating red meat daily increases your risk of heart disease, but I don’t believe it. My uncle was a rancher and he lived to be 100. His entire life he ate red meat three times a day. He didn’t die of a heart attack, either. He died when he fell down a well.”
This single story does not establish the presence or absence of causation.

12. Recap So what is the difference between Post Hoc and Cum Hoc?
Post Hoc is the assumption that the fact one event came after another establishes that it was caused by the other.
Cum Hoc is when we assume that two events that happen at about the same time establishes that one caused the other.