by ohthatpatrick Mon May 06, 2019 5:14 pm
The evidence shows that "If you were in an accident, you were less likely to be injured in a large car."
The shift in the conclusion to saying, "If you drive a large car, you are less likely to be injured in an accident", is making a different claim.
Say that you drive a big car and I drive a small one: if we each got into an accident, I would be more likely to get injured.
But also say, as (D) does, that you get into way more accidents than I do (my small car makes it easier to stop or swerve out of the way). When you add that to the equation, who is more likely to be injured:
you, who drives a large car and gets into frequent accidents (although usually doesn't get hurt in them)
or
me, who drives a small car and rarely gets into accidents (but would probably get hurt if I did get into one)?
It's possible that the large car driver overall has a higher chance of being injured than the small car driver.
Here's a different metaphor:
Some evil villain offers you this choice ...
1. you get tortured every time he flips a coin and it lands on heads.
or
2. you get tortured every time he rolls a six-sided die and it lands on 1 or 2.
Which choice would you take?
The 2nd of course. In the first one, I have a 50% chance of being tortured each time. In the 2nd one, I only have a 33.3% chance of being tortured.
But now say the evil villain goes on and says,
"you can choose either method, but you should know that I only plan to flip the coin twice, whereas I plan the roll the die ten times."
Now the 1st option sounds better.
The 1st option, high probability of pain but not as frequently occurring, is small car.
The 2nd option, low probability of pain but more frequently occurring, is large car.
The conclusion is flawed because without knowing how many accidents large cars vs. small cars are involved in, we don't know whether we'd be safer taking the "once in a while, but high chance of bad" or the "low chance of bad, but frequently occurring"
Does that make sense?