simpson’s paradox
I always had trouble understanding this.
Here I seek an example so I can finally get it. (I had trouble with Monty Hall problem too, until I came up with a satisfactory intuition)
| monty hall | simpson | |
|---|---|---|
| but my first choice was just as likely as the others! monty didn’t change the probability that my choice was correct | ||
| you’re right! he didn’t change the probability that your choice was correct. but he removed one option on the side of your 1st choice being wrong, thereby putting those two unchanged probabaili You always have 2/3 chance your first choice was wrong. That’s why you’re right that the probabilities don’t change. it’s just that now Monty put those 2/3 chance you were wrong into one option | ||
| monty gives you information |
“but monty didn’t change the probability that my first choice was correct!”
“that’s right, he didn’t”
“so then why should I switch?”
“well, why would you or anyone EVER switch?”
“I’d switch if it improved my chances”
“right. and what, again, is the chance you have of winning by not switching?”
“1/3, as always”
“yup” (and where is the other (1-1/3) 2 out of 3 chances now?)
“same place they were before! behind the other doors”
The “remaining door” is no longer “door #3”. In opening a door, “door #3” became “the door that is complement to my 1st choice”. MONTY DID CHANGE the probability that door #3 had the car. He DID NOT change the probability that your choice had the car.