I just have to put this here, math explanation from:
UMMM… It’s nice and stuff, the idea that they’re trying to convey here, but it’s a grave mistake to take just that population and think yourself done. If 0.2% of inmates were atheistic, but 0.1% of the general population was atheistic (it’s not the case), then that would mean atheists are more likely to commit crime.
But let’s do a quick estimate here. I want to find the probability that you’ll commit a crime, given that you’re an atheist:
We know that P(A|C) = 0.2%. Now we need the percentage of atheists in the general population (P(A)) and the probability that a random person will commit a crime (P(C)).
A few polls have taken place, and I don’t trust them entirely, because the rates have varied between 6% and 15% of Americans. I’ll take the neutral P(A) = 10% of Americans are atheists. The sources for these numbers can be found at the bottom of this page.
This alone is enough to give us an interesting likelihood ratio: the probability of being a criminal given you’re an atheist is about 0.02 times the probability of being a criminal in general. Moving on.
Now to find P(C), I’ll get the number that I found here, which says that “more than 1 in 100 adults in the US is in jail or prison,” so I’ll round that down to 1%.
Before we do the math, let me just be clear on the meaning of this. If you chose a random person in the USA and abducted them to your alien spaceship, without any bias, there would be a 1% chance that you’d get an inmate.
In that case, then, if you restricted your search to only atheists, 0.02% of them are inmates. P(C|A) = 0.02%.
The likelihood ratio of that is 1 criminal atheist for every 4,999 non-criminal atheists.
Another quick search found that around 77% of the population in the US are registered as Catholic/Protestant (there are probably less, because they likely don’t stop counting all the people who convert to other religions or become atheists), so the percentage in prison isn’t that different. You’ll get a probability of 0.96%.
Now, however, let’s go to the child molesters. I want the probability that someone is a molester, given that they’re Christian P(M|D) (I labelled Christianity D because C was already taken by criminality).
P(D|M) is given as 93%.
P(D) is 79.5%, according to this.
The likelihood ratio we found, then, is 1.17, which is to say that upon finding someone’s a Christian, you should be 1.17 times more certain that they’re child molesters.
According to this, there are 400.000 registered sex offenders in the US. So that’s P(M) = 0.13%.
Multiplying this together, the probability that someone is a sex offender given that they’re Christians is P(M|D) = 0.15%. Not much larger.
Throwing stats like these around isn’t really helpful. Probabilities have three degrees of freedom, and if you only give us one piece of the puzzle, we can’t really say anything at all!
As an extra, let’s find the Evidence shift caused by finding out someone’s religion. That is: once you find out someone is an atheist, how much evidence is that against them being a criminal? Once you find out someone is a Christian, how much evidence is that for them being child molesters?
We want, then, to find:
We know P(A|C) = 0.2% and P(D|M) = 93%. With some mathematics, we find that P(A|¬C) = 10.1% and P(D|¬M) = 79.49%.
Therefore, finding out someone is an atheist gives you 27 deciBels of evidence against their being criminals, while finding out someone is a Christian gives you only 0.7 deciBels of evidence for their being child molesters.
The main point of the post - atheists are in fact less likely to be criminals - is correct. But trying to throw around a lot of ugly-looking probabilities to impress people doesn’t help at all.
We’re already right. We don’t need to distort facts to make them look worse.
Although I confess that knowing people as I do, they probably didn’t even know what they were doing when they posted these numbers.
Important: I did not fact-check the numbers on the post, and all the numbers I’m using here were taken off quick Google searches. Once you plug in the numbers, however, the mathematics is sound.