Can someone explain its significance and maybe a simple example as well?
In: 3585
People wearing a motorcycle helmet are much more likely to be killed in a motorcycle crash than people not wearing a motorcycle helmet.
Does that mean that motorcycle helmets cause fatal motorcycle crashes?
No! If you look more closely at the data you’ll find that the crucial variable is whether or not the person is riding a motorcycle.
The association between helmets and fatal crashes is true when you look at the entire population, but that is because the vast majority of people not wearing a helmet are not at any risk of dying in a crash because they are not riding a motorcycle.
If you restrict the data to people riding motorcycles, you will find that those wearing helmets are less likely to die in a crash.
I’m going to steal [Skafi’s example](https://www.reddit.com/r/nba/comments/4p63ku/ysk_simpsons_paradox_and_basketball/):
Before getting to Simpson’s paradox, I’m going to define some basketball terms for anyone who is not familiar. In basketball, there are two types of field goal attempts. 2-pointers and 3-pointers. You can calculate their percentages individually or together as an overall field goal percentage. For example, let’s say that a player attempted 40 2-point field goals, making 30 of them, and attempted 10 3-point field goals, making 3 of them.
Her 2-point% is 30/40 = 75%.
Her 3-point% is 3/10 = 30%.
You can also look at overall field goal % by treating both types of shots the same and disregarding whether they were 2-point or 3-point attempts.
She attempted 50 total field goals (40 2-point + 10 3-point) and made a total of 33 (30 2-point + 3 3-point).
Her overall field goal % is then 33/50 = 66%.
An example of Simpson’s Paradox is the following. Say that you are told the 2-point% and 3-point% for two different players:
Player | 2-Point% | 3-Point% |
—————-|——-|——-|
Larry Bird | 50.9% | 37.6% |
Reggie Miller | 51.6% | 39.5% |
Reggie Miller’s % is higher than Larry Bird’s in both categories. The logical assumption would be that Reggie Miller’s combined field goal% would be higher than Larry Bird’s as well because that Reggie’s percentage is higher in both components of field goal%.
However, the actual values:
Player | 2-Point% | 3-Point% | Overall FG% |
—————-|——-|——-|————-|
Larry Bird | 50.9% | 37.6% | 49.6%
Reggie Miller | 51.6% | 39.5% | 47.1%
How can Larry Bird have a higher overall field goal % when he had a lower percentage for every component of the calculation? It’s because there was another factor not considered.
37% of Reggie Miller’s career field goal attempts were 3-Pointers, while only 10% of Larry Bird’s career field goal attempts were 3-Pointers. Because 3-point field goal attempts have a lower chance of success, Reggie’s 3-point % dragged his 2-point % further down than Larry’s 3-point % dragged his 2-Point % down.
The specific overall field goal% calculations:
Reggie Miller: 51.6%*63% + 39.5%*37% = 47.1%
Larry Bird: 50.9%*90% + 37.6%*10% = 49.6%
Again, you can see that Reggie’s overall field goal% was much more influenced by the relatively less likely 3-pointers than Larry’s was.
https://math.stackexchange.com/a/2216520
[More examples of Simpson’s Paradox, barring the ones on Wikipedia, Titanic, and delayed flights.](https://math.stackexchange.com/q/83756)
https://stats.stackexchange.com/questions/tagged/simpsons-paradox?tab=Frequent has a tag for Simpson’s paradox.
No ones is explaining it like hes 5.
It’s significance is that it reveals stats can be interpreted with seemingly contradictory results, depending on how you interpret them. Ie, you can use the same stats to support 2 dif sides of an argument.
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