The Book of Why Chapter 6 - Weekend Study Presentation

1. Causal Diagram in Wonderland
Book of Why Chapter 6

2. Four Paradoxes
• Monty Hall Problem
• Berkson’s Paradox
• Simson’s Paradox
• Lord’s Paradox

3. Monty Hall Problem
• Choose one door & Mr. Monty will open one goat door
which you didn’t choose
• Change your door will give you more chance to get the car?
Wiki : https://en.wikipedia.org/wiki/Monty_Hall_problem#/media/File:Monty_open_door.svg

4. Monty Hall Problem
• Chance to get right door at first place : 1/3
• Monty remove one wrong door
• If you change your choice then prob to choose right door
will be reversed : i.e. 1 - 1/3 = 2/3
• So if you change your choice then prob to get the car will be
doubled

5. Monty Hall Problem
• Let’s thinks other case…
• There is one thousand doors & when you choose door then
Mr. Monty open 998 wrong doors
• Will you change your choice?

6. Monty Hall Problem
• Let’s do Causal Diagram approach…
Your door
Location
of Car
independent
each other

7. Monty Hall Problem
• Let’s do Causal Diagram approach…
Your door
Location
of Car
Door
Opened
What a Collider?!
dependent
each other
Controlled…

8. Berkson’s Paradox
General Population Hospitalized in Last Six Months
Respiratory
Disease?
Bone disease? Bone disease?
Yes No % Yes Yes No % Yes
Yes 17 207 7.6 5 15 25.0
No (Control) 184 2,376 7.2 18 219 7.6
Bone
Disease
Respiratory
Hospitalization
?

9. Simson’s Paradox
• Simson’s reversal -> Simson’s paradox
• Simson’s reversal
• Easy ratio problem with different denominator
• A/B > a/b , C/D > c/d means (A+C)/(B+D) > (a+c)/(b+d) ?
• Simpson’s reversal is surprising to general people but not to
statisticians… but Simpson’s paradox is confusing to statisticians too
• Why?
Hits / At Bats
1995 1996 1997 All three years
David Justice 104/411 = .253 45/140 = .321 163/495 = .329 312/1,046 = .298
Drek Jeter 12/48 = .250 183/582 = .314 190/654 = .291 385/1,284 = .300

10. Simson’s Paradox
• Simson’s reversal -> Simson’s paradox
• Simson’s paradox
• “BBG problem” (bad, bad… but good total?)
• Savage’s “sure-thing principle”
• “better hitter?” : too simple word

11. Simson’s Paradox
Control group (No drug) Treatment Group (Took drug)
Heart attack No Heart attack Heart attack No Heart attack
Female 1 19 3 37
Male 12 28 8 12
Total 13 47 11 49
Gender
Drug
Heart
Attack

12. Simson’s Paradox
Control group (No drug) Treatment Group (Took drug)
Heart attack No Heart attack Heart attack No Heart attack
Low blood pressure 1 19 3 37
High blood pressure 12 28 8 12
Total 13 47 11 49
Blood
Pressure
Drug
Heart
Attack

13. Simson’s Paradox
• Easy to find out with continuous case

14. Lord’s Paradox
• Girl vs Boys ?
• Girl vs Boys… but just weight W0 case only?

15. Lord’s Paradox