# Question for the stats people

What is a good analogy for explaining that correlation does not mean causation? I’m looking for something that someone with the intellect of a 10 year old (my father-in-law) will be able to grasp. Thanks!

Sleeping with one’s shoes on is strongly correlated with waking up with a headache. Therefore, sleeping with one’s shoes on causes headache. The more firemen fighting a fire, the more damage there is going to be. Therefore firemen cause damage. With a decrease in the number of pirates we have seen an increase in global warming over the same time period. Therefore, global warming is caused by a lack of pirates. As ice cream sales increase, the rate of drowning deaths increases sharply. Therefore, ice cream causes drowning.

This guy sounds like a bald-faced idiot. You must have misgivings about marrying into his family.

Have him read Freakonomics. The last tornado destroyed 10 yellow houses, 7 red houses, and no blue houses. Paint your house blue and try to get a lower home insurance premium.

The three situations where correlation are not causation are: #1: Spurious Correlation: something like the blue houses example above. If you have 100 pairs of random variables, and use the traditional 95% confidence criterion, about 5 of them will be correlated, even though the numbers are completely random. #2: Correlation through a causally prior variable: this is like the firefighter example marakitus gave. The larger the fire, the greater the damage. The larger the fire, the more firemen are called. So firemen and damage are likely to be correlated, but reducing the number of firemen working on the fire will not cause the damage to go down (on average). A variation of #2 also happens a lot with variables that trend over time. This is like the pirates and global warming example. Both trend over time, and since time increases over time for both, they look more correlated than they really are. #3: Reverse causation: When people carry umbrellas it tends to rain. Maybe I can get it to rain less by selling fewer umbrellas. This one isn’t so much about correlation not equalling causation, as it is about making sure that your causation is in the correct direction.

I think Bchadwick’s response is good. The only thing I would add is that statistics can really only tell you about correlation. It is possible to talk about something Granger-causing another variable to change, which is probably the closest thing to causation in statistics. For X variable to Granger-cause Y you have to first look at Y and its lags. So you could look at monthly % changes for the S&P500 and regress it against like 13 lags. Then you could try to find a variable whose lagged values influence the % changes in S&P500, like say Industrial Production. If lagged variables of IP going back like 13 months are significant in an F-test and add value to the regression, you could say IP Granger-causes S&P500 returns. But even that doesn’t really mean causation. Causation works best in math, physics, and logic. IMHO, not so much in statistics.

Thanks all! I think I’ll use the firemen example. This is a result of my father-in-law calling at 1am to say “There is new info out that the government doesn’t want you to know. Vaccinations DO cause autism. So don’t get your son vaccinated!” He knows one person that blames their kids autism on vaccines. Then he went a surfin’ on the ole’ internet and got hooked on conspiracy theories (he called a couple weeks ago to tell us to get some cash because ALL the banks were closing down). The best is that he thinks we’re all going to die in 2012 (foretold in the Bible Code and by the Mayan calender) when a PLANET collides with the earth. That is, if the the bird flu doesn’t kill us all first.

Well… the correlation does not equal causation is good against the claim that vacinations CAUSE autism, it really doesn’t dispute the substance of his claim. He could still say that, fine, mercury-based vacinations are associated with higher levels of autism in some children. So you might still want to do some more research to dispute that. I would generally say that the scientists are still fighting about this, so there probably is no “truth” yet.

How about letting him know that vaccinations haven’t had mercury in them for years so he has nothing to worry about.