A few weeks ago, our family took a ferry across the English Channel. On the way from England to France, the ferry was extremely crowded, and the crossing took about 75 minutes. On the way back from France to England, there was hardly anyone on the ferry, and the captain announced that the crossing would take 95 minutes.
My 5-year old, wondering why the crossing was going to take longer on the way back, came up with this hypothesis:
“Maybe when there are less people, the boat goes slow; but when there are more people the boat goes faster.”
All the facts seemed to support her, and while this could be possible, I’ll hope you’ll agree that it wasn’t the most likely explanation. My 5-year-old had fallen prey to a classic statistical fallacy: correlation is not causation.
This phrase is so well known, that even people who don’t know anything about statistics often know this to be true. But the thing is, sometimes in science correlation is all you’ve got.
The official name for this type of logical fallacy is “Cum hoc ergo propter hoc,” or “with this, therefore because of this.” According to my daughter’s reasoning, after fewer people got on the ferry, the trip took longer. Therefore the trip took longer because fewer people got on the ferry.
It’s easy to see the problem with that logic in these examples:
“After I washed my car, it rained. Therefore washing my car causes rain.”
“When I got in the bath tub, the phone rang. Therefore getting in the bath will lead to the phone ringing.”
“We won our baseball game when I was wearing these socks, so it must be the lucky socks that caused our win.”